Nanoelectronics – theory and simulation


A. Vegliante, S. Fernandez, R. Ortiz, M. Vilas-Varela, T. Baum, N. Friedrich, F. Romero-Lara, A. Aguirre, K. Vaxevani, D. Wang, C. Garcia, H. S. J. van der Zant, T. Frederiksen, D. Peña, and J. I. Pascual
Tuning the spin interaction in non-planar organic diradicals through mechanical manipulation
submitted [arXiv:2402.08641]

Open-shell polycyclic aromatic hydrocarbons (PAHs) represent promising building blocks for carbon-based functional magnetic materials. Their magnetic properties stem from the presence of unpaired electrons localized in radical states of π character. Consequently, these materials are inclined to exhibit spin delocalization, form extended collective states, and respond to the flexibility of the molecular backbones. However, they are also highly reactive, requiring structural strategies to protect the radical states from reacting with the environment. Here, we demonstrate that the open-shell ground state of the diradical 2-OS survives on a Au(111) substrate as a global singlet formed by two unpaired electrons with anti-parallel spins coupled through a conformational dependent interaction. The 2-OS molecule is a protected derivative of the Chichibabin's diradical, featuring a non-planar geometry that destabilizes the closed-shell quinoidal structure. Using scanning tunneling microscopy (STM), we localized the two interacting spins at the molecular edges, and detected an excited triplet state a few millielectronvolts above the singlet ground state. Mean-field Hubbard simulations reveal that the exchange coupling between the two spins strongly depends on the torsional angles between the different molecular moieties, suggesting the possibility of influencing the molecule's magnetic state through structural changes. This was demonstrated here using the STM tip to manipulate the molecular conformation, while simultaneously detecting changes in the spin excitation spectrum. Our work suggests the potential of these PAHs for a new class of all-carbon spin-crossover materials.

S. Jiang, F. Scheurer, Q. Sun, P. Ruffieux, X. Yao, A. Narita, K. Müllen, R. Fasel, T. Frederiksen, and G. Schull
Length-independent quantum transport through topological band states of graphene nanoribbons
submitted [arXiv:2208.03145] [HTML5]

Atomically precise graphene nanoribbons (GNRs) have emerged as promising candidates for nanoelectronic applications due to their widely tunable energy band gaps resulting from lateral quantum confinement and edge effects. Here we report on the electronic transport characterization of an edge-modified GNR suspended between the tip of a scanning tunneling microscope (STM) and a Au(111) substrate. Differential conductance measurements on this metal-GNR-metal junction reveal loss-less transport properties (inverse decay length β<0.001Å) with high conductance (0.1 G0) at low voltages (50 meV) over long distances (z>10 nm). The transport behavior is sensitive to the coupling between ribbon and electrodes, an effect that is rationalized using tight-binding and density functional theory simulations. From extensive modelling we infer that the length-independent transport is a manifestation of band transport through topological valence states, which originate from the zigzag segments on the GNR edges.

M. Alkorta, R. Cizek, N. Néel, T. Frederiksen, and J. Kröger
Impact of single-melamine tautomerization on the excitation of molecular vibrations in inelastic electron tunneling spectroscopy
Nano Lett., in press (2024) [ PDF ] [DOI]

Vibrational quanta of melamine and its tautomer are analyzed at the single-molecule level on Cu(100) with inelastic electron tunneling spectroscopy. The on-surface tautomerization gives rise to markedly different low-energy vibrational spectra of the isomers, as evidenced by a shift in mode energies and a variation in inelastic cross sections. Spatially resolved spectroscopy reveals the maximum signal strength on an orbital nodal plane, excluding resonant inelastic tunneling as the mechanism underlying the quantum excitations. Decreasing the probe–molecule separation down to the formation of a chemical bond between the melamine amino group and the Cu apex atom of the tip leads to a quenched vibrational spectrum with different excitation energies. Density functional and electron transport calculations reproduce the experimental findings and show that the shift in the quantum energies applies to internal molecular bending modes. The simulations moreover suggest that the bond formation represents an efficient manner of tautomerizing the molecule.

S. Mishra, M. Vilas-Varela, L.-A. Lieske, R. Ortiz, S. Fatayer, I. Rončević, F. Albrecht, T. Frederiksen, D. Peña, and L. Gross
Bistability between π-diradical open-shell and closed-shell states in indeno[1,2-a]fluorene
Nat. Chem. 16, 755-761 (2024) [ PDF ] [DOI] [arXiv:2303.04483] [HTML5]

Indenofluorenes are non-benzenoid conjugated hydrocarbons that have received great interest owing to their unusual electronic structure and potential applications in non-linear optics and photovoltaics. Here, we report the generation of unsubstituted indeno[1,2-a]fluorene, the final and yet unreported parent indenofluorene regioisomer, on various surfaces by cleavage of two C-H bonds in 7,12-dihydro indeno[1,2-a]fluorene through voltage pulses applied by the tip of a combined scanning tunneling microscope and atomic force microscope. On bilayer NaCl on Au(111), indeno[1,2-a]fluorene is in the neutral charge state, while it exhibits charge bistability between neutral and anionic states on the lower work function surfaces of bilayer NaCl on Ag(111) and Cu(111). In the neutral state, indeno[1,2-a]fluorene exhibits either of two ground states: an open-shell π-diradical state, predicted to be a triplet by density functional and multireference many-body perturbation theory calculations, or a closed-shell state with a para-quinodimethane moiety in the as-indacene core. Switching between open- and closed-shell states of a single molecule is observed by changing its adsorption site on NaCl.

J. Hieulle, C. Garcia Fernandez, N. Friedrich, A. Vegliante, S. Sanz, D. Sanchez-Portal, M. Haley, J. Casado, T. Frederiksen, J. I. Pascual
From solution to surface: Persistence of the diradical character of a diindenoanthracene derivative on a metallic substrate
J. Phys. Chem. Lett. 14, 11506 (2023) [ PDF ] [DOI]

Organic diradicals are envisioned as elementary building blocks for designing a new generation of spintronic devices and have been used in constructing prototypical field effect transistors and non-linear optical devices. Open-shell systems, however, are also reactive, thus requiring design strategies to "protect" their radical character from the environment, especially when they are embedded into solid-state devices. Here, we report the persistence on a metallic surface of the diradical character of a diindeno[b,i]anthracene (DIAn) core protected by bulky end-groups. Our scanning tunneling spectroscopy measurements on single-molecules detected singlet-triplet excitations that were absent for DIAn species packed in assembled structures. Density functional theory simulations unravel that molecular geometry on the metal substrate can crucially modify the value of the single-triplet gap via the delocalization of the radical sites. The persistence of the diradical character over metallic substrates is a promising finding for integrating radical-based materials in functional devices.

J. Brede, N. Merino-Díez, A. Berdonces, S. Sanz, A. Domínguez-Celorrio, J. Lobo-Checa, M. Vilas-Varela, D. Peña, T. Frederiksen, J. I. Pascual, D. G. de Oteyza, and D. Serrate
Detecting the spin-polarization of edge states in graphene nanoribbons
Nat. Commun. 14, 6677 (2023) [ PDF ] [DOI] [arXiv:2301.11370] [HTML5]

Low dimensional carbon-based materials are interesting because they can show intrinsic π-magnetism associated to p-electrons residing in specific open-shell configurations. Consequently, during the last years there have been impressive advances in the field combining indirect experimental fingerprints of localized magnetic moments with theoretical models. In spite of that, a characterization of their spatial- and energy-resolved spin-moment has so far remained elusive. To obtain this information, we present an approach based on the stabilization of the magnetization of π-orbitals by virtue of a supporting substrate with ferromagnetic ground state. Remarkably, we go beyond localized magnetic moments in radical or faulty carbon sites: In our study, energy-dependent spin-moment distributions have been extracted from spatially extended one-dimensional edge states of chiral graphene nanoribbons. This method can be generalized to other nanographene structures, representing an essential validation of these materials for their use in spintronics and quantum technologies.

N. Okabayashi, T. Frederiksen, A. Liebig, and F. J. Giessibl
Dynamic friction unraveled by observing an unexpected intermediate state in controlled molecular manipulation
Phys. Rev. Lett. 131, 148001 (2023) [ PDF ] [DOI] [arXiv:2112.12286] [HTML5]

The pervasive phenomenon of friction has been studied at the nanoscale via a controlled manipulation of single atoms and molecules with a metallic tip, which enabled a precise determination of the static friction force necessary to initiate motion. However, little is known about the atomic dynamics during manipulation. Here we reveal the complete manipulation process of a CO molecule on a Cu(110) surface at low temperatures using a combination of non-contact atomic force microscopy and density functional theory simulations. We found that an intermediate state, inaccessible for the far-tip position, is enabled in the reaction pathway for the close-tip position, which is crucial to understand the manipulation process including dynamic friction. Our results show how friction forces can be controlled and optimized, facilitating new fundamental insights for tribology.

N. Okabayashi, T. Frederiksen, A. Liebig, and F. J. Giessibl
Energy dissipation of a carbon monoxide molecule manipulated using a metallic tip on copper surfaces (Editors' suggestion )
Phys. Rev. B 108, 165401 (2023) [ PDF ] [DOI] [arXiv:2112.12286] [HTML5]

Friction is a familiar phenomenon to humankind and has long been studied, however, it is fundamentally difficult to understand because of the complex processes that contributes to it. For elucidating friction, it is helpful to simplify the system. In this respect, molecular manipulation, in which a single molecule or atom on a surface is moved by the tip of a scanning probe microscope, is an ideal research target. In this study, we combined non-contact atomic force microscopy, inelastic electron tunneling spectroscopy, and density functional theory calculations to investigate the molecular manipulation process of a single CO molecule on Cu(110) and Cu(111) surfaces at low temperature. We discovered the presence of a metastable adsorption site that is not occupied when the tip is far from the surface, but is engaged for close tip positions. This adsorption site plays the role of an intermediate state in the reaction path of manipulation, and this intermediate is important for understanding the dynamics of manipulation and dynamic friction. We elaborate the process leading to the above conclusions in detail and discuss future perspectives.

Q. Du, X. Su, Y. Liu, Y. Jiang, C. Li, K. Yan, R. Ortiz, T. Frederiksen, S. Wang, and P. Yu
Orbital-symmetry effects on magnetic exchange in open-shell nanographenes
Nat. Commun. 14, 4802 (2023) [ PDF ] [DOI] [Research Square preprint]

Open-shell nanographenes appear as promising candidates for future applications in spintronics and quantum technologies. A critical aspect to realize this potential is to design and control the magnetic exchange. Here, we reveal the effects of frontier orbital symmetries on the magnetic coupling in diradical nanographenes through scanning probe microscope measurements and different levels of theoretical calculations. In these open-shell nanographenes, the exchange energy exhibits a remarkable variation between 20 and 160 meV. Theoretical calculations reveal that frontier orbital symmetries play a key role in affecting the magnetic coupling on such a large scale. Moreover, a triradical nanographene is demonstrated for investigating the magnetic interaction among three unpaired electrons with unequal magnetic exchange, in agreement with Heisenberg spin model calculations. Our results provide insights into both theoretical design and experimental realization of nanographene materials with different exchange interactions through tuning the orbital symmetry, potentially useful for realizing magnetically operable graphene-based nanomaterials.

S. Sengupta, T. Frederiksen, and G. Giedke
Hyperfine interactions in open-shell planar sp2-carbon nanostructures
Phys. Rev. B 107, 224433 (2023) [ PDF ] [DOI] [arXiv:2303.11422] [HTML5]

We investigate hyperfine interaction (HFI) using density-functional theory for several open-shell planar sp2-carbon nanostructures displaying π-magnetism. Our prototype structures include both benzenoid ([n]triangulenes and a graphene nanoribbon) as well as non-benzenoid (indene, fluorene, and indene[2,1-b]fluorene) molecules. Our results obtained with ORCA indicate that isotropic Fermi contact and anisotropic dipolar terms contribute in comparable strength, rendering the HFI markedly anisotropic. We find that the magnitude of HFI in these molecules can reach more than 100 MHz, thereby opening up the possibility of experimental detection via methods such as electron spin resonance-scanning tunneling microscopy (ESR-STM). Additionally, we use empirical models based on π-spin polarization at carbon sites to provide generic sp2 HFI fit parameters for these classes of molecules using methods such as ORCA, SIESTA and mean-field Hubbard (MFH) models that successfully describe the Fermi contact and dipolar contributions for 13C and 1H nuclei. These fit parameters allow to obtain hyperfine tensors for large systems where existing methodology is not suitable or computationally too expensive. As an example, we show how HFI scales with system size in [n]triangulenes for large n using MFH. We also discuss some implications of HFI for electron-spin decoherence and for coherent nuclear dynamics.

S. Sanz, N. Papior, G. Giedke, D. Sanchez-Portal, M. Brandbyge, and T. Frederiksen
Mach–Zehnder-like interferometry with graphene nanoribbon networks
J. Phys.: Condens. Matter 35, 374001 (2023) [ PDF ] [DOI] [arXiv:2302.04821] [HTML5]

We study theoretically electron interference in a Mach–Zehnder-like geometry formed by four zigzag graphene nanoribbons (ZGNRs) arranged in parallel pairs, one on top of the other, such that they form intersection angles of 60˚ Depending on the interribbon separation, each intersection can be tuned to act either as an electron beam splitter or as a mirror, enabling tuneable circuitry with interfering pathways. Based on the mean-field Hubbard model and Green's function techniques, we evaluate the electron transport properties of such 8-terminal devices and identify pairs of terminals that are subject to self-interference. We further show that the scattering matrix formalism in the approximation of independent scattering at the four individual junctions provides accurate results as compared with the Green's function description, allowing for a simple interpretation of the interference process between two dominant pathways. This enables us to characterize the device sensitivity to phase shifts from an external magnetic flux according to the Aharonov–Bohm effect as well as from small geometric variations in the two path lengths. The proposed devices could find applications as magnetic field sensors and as detectors of phase shifts induced by local scatterers on the different segments, such as adsorbates, impurities or defects. The setup could also be used to create and study quantum entanglement.

R. Ortiz, G. Giedke, and T. Frederiksen
Magnetic frustration and fractionalization in oligo(indenoindenes)
Phys. Rev. B 107, L100416 (2023) [ PDF ] [DOI] [arXiv:2211.07385] [HTML5]

Oligo(indenoindenes)(OInIn) are π-conjugated ladder carbon polymers with alternating hexagons and pentagons, hosting one unpaired electron for each of the latter in the open-shell limit. Here we study the main magnetic interactions in finite OInIn, classifying the six possible isomers in two different classes of three isomers each. We find that one class can be described by frustrated S=1/2 Heisenberg chains, with antiferromagnetic interactions between the second-neighbour sites. The other class is characterized by antiferromagnetic order. Employing several levels of theory we further show that the ground state of one of the isomers is a valence-bond solid (VBS) of ferromagnetic dimers (S=1). This is topologically similar to that of the Affleck-Kennedy-Lieb-Tasaki (AKLT) model, which is known to show fractional S=1/2 states at the edges.

D. G. de Oteyza and T. Frederiksen
Carbon-based nanostructures as a versatile platform for tunable π-magnetism (Topical Review)
J. Phys.: Condens. Matter 34, 443001 (2022) [ PDF ] [DOI] [arXiv:2206.12981] [HTML5]

Emergence of π-magnetism in open-shell nanographenes has been theoretically predicted decades ago but their experimental characterization was elusive due to the strong chemical reactivity that makes their synthesis and stabilization difficult. In recent years, on-surface synthesis under vacuum conditions has provided unprecedented opportunities for atomically precise engineering of nanographenes, which in combination with scanning probe techniques have led to a substantial progress in our capabilities to realize localized electron spin states and to control electron spin interactions at the atomic scale. Here we review the essential concepts and the remarkable advances in the last few years, and outline the versatility of carbon-based π-magnetic materials as an interesting platform for applications in spintronics and quantum technologies.

S. Sanz, N. Papior, G. Giedke, D. Sánchez-Portal, M. Brandbyge, and T. Frederiksen
Spin-polarizing electron beam splitter from crossed graphene nanoribbons
Phys. Rev. Lett. 129, 037701 (2022) [ PDF ] [DOI] [arXiv:2201.07147] [HTML5]

Junctions composed of two crossed graphene nanoribbons (GNRs) have been theoretically proposed as electron beam splitters where incoming electron waves in one GNR can be split coherently into propagating waves in two outgoing terminals with nearly equal amplitude and zero back-scattering. Here we scrutinize this effect for devices composed of narrow zigzag GNRs taking explicitly into account the role of Coulomb repulsion that leads to spin-polarized edge states within mean-field theory. We show that the beam-splitting effect survives the opening of the well-known correlation gap and, more strikingly, that a spin-dependent scattering potential emerges which spin-polarizes the transmitted electrons in the two outputs. A near-perfect polarization can be achieved by joining several junctions in series. Our findings suggest that GNRs are interesting building blocks in spintronics and quantum technologies with applications for interferometry and entanglement.

T. Wang, S. Sanz, J. Castro-Esteban, J. Lawrence, A. Berdonces-Layunta, M. S. G. Mohammed, M. Vilas-Varela, M. Corso, D. Peña, T. Frederiksen, and D. G. de Oteyza
Magnetic interactions between radical pairs in chiral graphene nanoribbons
Nano Lett. 22, 164-171 (2022) [ PDF ] [arXiv:2108.13473]

Magnetic graphene nanoribbons (GNRs) have become promising candidates for future applications, including quantum technologies. Here, we characterize magnetic states hosted by chiral graphene nanoribbons (chGNRs). The substitution of a hydrogen atom at the chGNR edge by a ketone group effectively adds one pz electron to the π-electron network, thus producing an unpaired π radical. A closely related scenario occurs for regular ketone-functionalized chGNRs in which one oxygen atom is missing. Two such radical states can interact via exchange coupling and we study those interactions as a function of their relative position, which includes a remarkable dependence on the chirality, as well as on the nature of the surrounding GNR, i.e., with or without ketone functionalization. In addition, we determine the parameters whereby this type of systems with oxygen heteroatoms can be adequately described within the widely used mean-field Hubbard model. Altogether, we provide new insights to both theoretically model and devise GNR-based nanostructures with tunable magnetic properties.

R. Avriller, Q. Schaeverbeke, T. Frederiksen, and F. Pistolesi
Photon-emission statistics induced by electron tunnelling in plasmonic nanojunctions
Phys. Rev. B 104, L241403 (2021) [ PDF ] [DOI] [arXiv:2107.07860] [HTML5]

We investigate the statistics of photons emitted by tunneling electrons in a single electronic level plasmonic nanojunction. We compute the waiting-time distribution of successive emitted photons w(τ). When the cavity damping rate κ is larger than the electronic tunneling rate Γ, we show that in the photon-antibunching regime, w(τ) indicates that the average delay time between two successive photon-emission events is given by 1/Γ. This is in contrast with the usually considered second-order correlation function of emitted photons, g(2)(τ), which displays the single time scale 1/κ. Our analysis shows a relevant example for which w(τ) gives independent information on the photon-emission statistics with respect to g(2)(τ), leading to physical insight into the problem. We discuss how this information can be extracted from experiments even in the presence of a nonperfect photon-detection yield.

J. Hieulle, S. Castro, N. Friedrich, A. Vegliante, F. Romero Lara, S. Sanz, D. Rey, M. Corso, T. Frederiksen, J. I. Pascual, and D. Peña
On-surface synthesis and collective spin excitations of a triangulene-based nanostar
Angew. Chem. Int. Ed. 60, 25224-25229 (2021) [ PDF ] [arXiv:2107.02198]

Triangulene nanographenes are open-shell molecules with predicted high spin state due to the frustration of their conjugated network. Their long-sought synthesis became recently possible over a metal surface. Here, we present a macrocycle formed by six [3]triangulenes, which was obtained by combining the solution synthesis of a dimethylphenyl-anthracene cyclic hexamer and the on-surface cyclodehydrogenation of this precursor over a gold substrate. The resulting triangulene nanostar exhibits a collective spin state generated by the interaction of its 12 unpaired π-electrons along the conjugated lattice, corresponding to the antiferromagnetic ordering of six S = 1 sites (one per triangulene unit). Inelastic electron tunneling spectroscopy resolved three spin excitations connecting the singlet ground state with triplet states. The nanostar behaves close to predictions from the Heisenberg model of a S = 1 spin ring, representing a unique system to test collective spin modes in cyclic systems.

J. Li, S. Sanz, N. Merino-Díez, M. Vilas-Varela, A. Garcia-Lekue, M. Corso, D. G. de Oteyza, T. Frederiksen, D. Peña, and J. I. Pascual
Topological phase transition in chiral graphene nanoribbons: from edge bands to end states
Nat. Commun. 12, 5538 (2021) [ PDF ] [arXiv:2103.15937] [HTML5]

Precise control over the size and shape of graphene nanostructures allows engineering spin-polarized edge and topological states, representing a novel source of non-conventional π-magnetism with promising applications in quantum spintronics. A prerequisite for their emergence is the existence of robust gapped phases, which are difficult to find in extended graphene systems. Here we show that semi-metallic chiral GNRs (chGNRs) narrowed down to nanometer widths undergo a topological phase transition. We fabricated atomically precise chGNRs of different chirality and size by on surface synthesis using predesigned molecular precursors. Combining scanning tunneling microscopy (STM) measurements and theory simulations, we follow the evolution of topological properties and bulk band gap depending on the width, length, and chirality of chGNRs. Our findings represent a new platform for producing topologically protected spin states and demonstrate the potential of connecting chiral edge and defect structure with band engineering.

T. Frederiksen
Bimetallic electrodes boost molecular junctions
Nat. Mater., News & Views (2021) [ PDF ]

Deposition of a one-atom-thick layer of Ag or Cu on Au electrodes proves to be an effective strategy to tune the band alignment and conductivity of molecular junctions.

N. Friedrich, P. Brandimarte, J. Li, S. Saito, S. Yamaguchi, I. Pozo, D. Peña, T. Frederiksen, A. Garcia-Lekue, D. Sánchez-Portal, and J. I. Pascual
Magnetism of topological boundary states induced by boron substitution in graphene nanoribbons
Phys. Rev. Lett. 125, 146801 (2020) [ PDF ] [PRL Cover] [arXiv:2004.10280] [HTML5]

Graphene nanoribbons (GNRs), low-dimensional platforms for carbon-based electronics, show the promising perspective to also incorporate spin polarization in their conjugated electron system. However, magnetism in GNRs is generally associated to localized states around zigzag edges, difficult to fabricate and with high reactivity. Here we demonstrate that magnetism can also be induced away from physical GNR zigzag edges through atomically precise engineering topological defects in its interior. A pair of substitutional boron atoms inserted in the carbon backbone breaks the conjugation of their topological bands and builds two spin-polarized boundary states around. The spin state was detected in electrical transport measurements through boron-substituted GNRs suspended between tip and sample of a scanning tunneling microscope. First-principle simulations find that boron pairs induce a spin 1, which is modified by tuning the spacing between pairs. Our results demonstrate a route to embed spin chains in GNRs, turning them basic elements of spintronic devices.

S. Sanz, P. Brandimarte, G. Giedke, D. Sánchez-Portal, and T. Frederiksen
Crossed graphene nanoribbons as beam splitters and mirrors for electron quantum optics
Phys. Rev. B 102, 035436 (2020) [ PDF ] [arXiv:2005.11391] [HTML5]

We analyze theoretically 4-terminal electronic devices composed of two crossed graphene nanoribbons (GNRs) and show that they can function as beam splitters or mirrors. These features are identified for electrons in the low-energy region where a single valence or conduction band is present. Our modeling is based on pz orbital tight-binding with Slater-Koster type matrix elements fitted to accurately reproduce the low-energy bands from density functional theory calculations. We analyze systematically all devices that can be constructed with either zigzag or armchair GNRs in AA and AB stackings. From Green's function theory the elastic electron transport properties are quantified as a function of the ribbon width. We find that devices composed of relatively narrow zigzag GNRs and AA-stacked armchair GNRs are the most interesting candidates to realize electron beam splitters with a close to 50-50 ratio in the two outgoing terminals. Structures with wider ribbons instead provide electron mirrors, where the electron wave is mostly transferred into the outgoing terminal of the other ribbon, or electron filters where the scattering depends sensitively on the wavelength of the propagating electron. We also test the robustness of these transport properties against variations in intersection angle, stacking pattern, lattice deformation (uniaxial strain), inter-GNR separation, and electrostatic potential differences between the layers. These generic features show that GNRs are interesting basic components to construct electronic quantum optical setups.

W. Schattke, T. Frederiksen, M.A. Van Hove, and R. Díez Muiño
Nanomechanics of a hydrogen molecule suspended between two equally charged tips
Phys. Rev. B 101, 195436 (2020) [ PDF ] [arXiv:1910.11619] [HTML5]

The geometric configuration and energy of a hydrogen molecule centered between two point-shaped tips of equal charge are calculated with the variational quantum Monte Carlo (QMC) method without the restriction of the Born-Oppenheimer (BO) approximation. The ground-state nuclear distribution, stability, and low-vibrational excitations are found to deviate significantly from the BO treatment based on a potential energy surface obtained with the same QMC accuracy. The quantum-mechanical distribution of the molecular axis direction and the bond length at a subnanometer level is fundamental for understanding nanomechanical dynamics with embedded hydrogen. The cylindrical symmetry of the tip arrangement yields a uniform azimuthal distribution of the molecular axis vector relative to the tip-tip axis. For fixed tip separation, the QMC sampling shows that the polar angle distribution of the molecular axis is centered around the equatorial plane for positive tip charge (transverse alignment) and around the tip-tip direction for negative tip charge (bridge alignment). These deviations from spherical symmetry are magnified as the tip-tip distance decreases. Our results thus show that the molecular orientation in the junction can be controlled by the tip charge and separation, suggesting an application in the field of molecular machines.

J. Li, S. Sanz, J. Castro-Esteban, M. Vilas-Varela, N. Friedrich, T. Frederiksen, D. Peña, and J. I. Pascual
Uncovering the triplet ground state of triangular graphene nanoflakes engineered with atomic precision on a metal surface
Phys. Rev. Lett. 124, 177201 (2020) [ PDF ] [DOI] [arXiv:1912.08298] [HTML5]

Graphene can develop large magnetic moments in custom-crafted open-shell nanostructures such as triangulene, a triangular piece of graphene with zigzag edges. Current methods of engineering graphene nanosystems on surfaces succeeded in producing atomically precise open-shell structures, but demonstration of their net spin remains elusive to date. Here, we fabricate triangulenelike graphene systems and demonstrate that they possess a spin S=1 ground state. Scanning tunneling spectroscopy identifies the fingerprint of an underscreened S=1 Kondo state on these flakes at low temperatures, signaling the dominant ferromagnetic interactions between two spins. Combined with simulations based on the meanfield Hubbard model, we show that this S=1 π paramagnetism is robust and can be turned into an S=1/2 state by additional H atoms attached to the radical sites. Our results demonstrate that π paramagnetism of high-spin graphene flakes can survive on surfaces, opening the door to study the quantum behavior of interacting π spins in graphene systems.

T. Jasper-Toennies, M. Gruber, S. Johannsen, T. Frederiksen, A. Garcia-Lekue, T. Jäkel, F Roehricht, R. Herges, and R. Berndt
Rotation of Ethoxy and Ethyl Moieties on a Molecular Platform on Au(111)
ACS Nano 14, 3907-3916 (2020) [ PDF ] [DOI]

Molecular rotors have attracted considerable interest for their prospects in nanotechnology. However, their adsorption on supporting substrates, where they may be addressed individually, usually modifies their properties. Here, we investigate the switching of two closely-related three-states rotors mounted on platforms on Au(111) using low-temperature scanning tunneling microscopy and density functional theory calculations. Being physisorbed the platforms retain important gas-phase properties of the rotor. This simplifies a detailed analysis, and permits, for instance, the identification of the vibrational modes involved in the rotation process. The symmetry provided by the platform enables active control of the rotation direction through electrostatic interactions with the tip and charged neighboring adsorbates. The present investigation of two model systems may turn out useful for designing platforms that provide directional rotation and for transferring more sophisticated molecular machines from the gas-phase to surfaces.

Q. Schaeverbeke, R. Avriller, T. Frederiksen and F. Pistolesi
Single-photon emission mediated by single-electron tunneling in plasmonic nanojunctions
Phys. Rev. Lett. 123, 246601 (2019) [ PDF ] [arXiv:1907.11269] [HTML5]

Recent scanning tunnelling microscopy (STM) experiments reported single-molecule fluorescence induced by tunneling currents in the nanoplasmonic cavity formed by the STM tip and the substrate.The electric field of the cavity mode couples with the current-induced charge fluctuations of the molecule, allowing the excitation of the mode. We investigate theoretically this system for the experimentally relevant limit of large damping rate \kappa for the cavity mode and arbitrary coupling strength to a single-electronic level. We find that for bias voltages close to the first inelastic threshold of photon emission, the emitted light displays anti-bunching behavior with vanishing second-order photon correlation function. At the same time, the current and the intensity of emitted light display Franck--Condon steps at multiples of the cavity frequency \omega_c with a width controlled by kappa rather than the temperature T. For large bias voltages, we predict strong photon bunching of the order of the \kappa/\Gamma where \Gamma is the electronic tunneling rate. Our theory thus predicts that strong coupling to a single level allows current-driven non-classical light emission.

M. Mohr, T. Jasper-Toennies, T. Frederiksen, A. Garcia-Lekue, S. Ulrich, R. Herges, and R. Berndt
Conductance channels of a platform molecule on Au(111) probed with shot noise
Phys. Rev. B 99, 245417 (2019) [ PDF ] [DOI] [arXiv:1905.08591] [HTML5]

The shot noise of the current I through junctions to single trioxatriangulenium cations (TOTA+) on Au(111) is measured with a low temperature scanning tunneling microscope using Au tips. The noise is significantly reduced compared to the Poisson noise power of 2eI and varies linearly with the junction conductance. The data are consistent with electron transmission through a single spin-degenerate transport channel and show that TOTA+ in a Au contact does not acquire an unpaired electron. Ab initio calculations reproduce the observations and show that the current involves the lowest unoccupied orbital of the molecule and tip states close to the Fermi level.

M. Kolmer, P. Brandimarte, J. Lis, R. Zuzak, S. Godlewski, H. Kawai, A. Garcia-Lekue, N. Lorente, T. Frederiksen, C. Joachim, D. Sanchez-Portal, and M. Szymonski
Electronic transport in planar atomic-scale structures measured by two-probe scanning tunneling spectroscopy
Nat. Commun. 10, 1573 (2019) [ PDF ] [DOI]

Miniaturization of electronic circuits into the single-atom level requires novel approaches to characterize transport properties. Due to its unrivaled precision, scanning probe microscopy is regarded as the method of choice for local characterization of atoms and single molecules supported on surfaces. Here we investigate electronic transport along the anisotropic germanium (001) surface with the use of two-probe scanning tunneling spectroscopy and first-principles transport calculations. We introduce a method for the determination of the transconductance in our two-probe experimental setup and demonstrate how it captures energy-resolved information about electronic transport through the unoccupied surface states. The sequential opening of two transport channels within the quasi-one-dimensional Ge dimer rows in the surface gives rise to two distinct resonances in the transconductance spectroscopic signal, consistent with phase-coherence lengths of up to 50 nm and anisotropic electron propagation. Our work paves the way for the electronic transport characterization of quantum circuits engineered on surfaces.

T. Jasper-Toennies, A. Garcia-Lekue, T. Frederiksen, S. Ulrich, R. Herges and R. Berndt
High-conductance contacts to functionalized molecular platforms physisorbed on Au(111)
J. Phys.: Condens. Matter 31, 18LT01 (2019) [ PDF ] [DOI]

The conductances of molecules physisorbed to Au(111) via an extended π system are probed with the tip of a low-temperature scanning tunneling microscope to maximize the control of the junction geometry. Inert hydrogen, methyl, and reactive propynyl subunits were attached to the platform and stand upright. Because of their different reactivities, either non-bonding (hydrogen and methyl) or bonding (propynyl) tip-molecule contacts are formed. The conductances exhibit little scatter between different experimental runs on different molecules, display distinct evolutions with the tip-subunit distance, and reach contact values of 0.003-0.05 G0. For equal tip-platform distances the contact conductance of the inert methyl is close to that of the reactive propynyl. Under further compression, the inert species, hydrogen and methyl, are found to be better conductors. This shows that the current flow is not directly correlated with the chemical interaction. Atomistic calculations for the methyl case reproduce the conductance evolution and reveal the role of the junction geometry, forces and orbital symmetries at the tip-molecule interface. The current flow is controlled by orbital symmetries at the electrode interfaces rather than by the energy alignment of the molecular orbitals and electrode states. Functionalized molecular platforms thus open new ways to control and engineer electron conduction through metal-molecule interfaces at the atomic level.

J. Li, S. Sanz, M. Corso, D. J. Choi, D. Peña, T. Frederiksen, and J. I. Pascual
Single spin localization and manipulation in graphene open-shell nanostructures
Nat. Commun. 10, 200 (2019) [ PDF ] [DOI] [arXiv:1808.07532] [HTML5]

Turning graphene magnetic is a promising challenge to make it an active material for spintronics. Predictions state that graphene structures with specific shapes can spontaneously develop magnetism driven by Coulomb repulsion of π-electrons, but its experimental verification is demanding. Here, we report on the observation and manipulation of individual magnetic moments in graphene open-shell nanostructures on a gold surface. Using scanning tunneling spectroscopy, we detect the presence of single electron spins localized around certain zigzag sites of the carbon backbone via the Kondo effect. We find near-by spins coupled into a singlet ground state and quantify their exchange interaction via singlet-triplet inelastic electron excitations. Theoretical simulations picture how electron correlations result in spin-polarized radical states with the experimentally observed spatial distributions. Extra hydrogen atoms bound to radical sites quench their magnetic moment and switch the spin of the nanostructure in half-integer amounts. Our work demonstrates the intrinsic π-paramagnetism of graphene nanostructures.

G. Calogero, N. R. Papior, B. Kretz, A. Garcia-Lekue, T. Frederiksen, and M. Brandbyge
Electron transport in nanoporous graphene: Probing the Talbot effect
Nano Lett. 19, 576-581 (2019) [ PDF ] [DOI] [arXiv:1811.07576] [HTML5]

Electrons in graphene can show diffraction and interference phenomena fully analogous to light thanks to their Dirac-like energy dispersion. However it is not clear how this optical analogy persists in nanostructured graphene, e.g. with pores. Nanoporous graphene (NPG) consisting of linked graphene nanoribbons has recently been fabricated using molecular precursors and bottom-up assembly [Moreno et al, Science 360, 199 (2018)]. We predict that electrons propagating in NPG exhibit the interference Talbot effect, analogous to photons in coupled waveguides. Our results are obtained by parameter-free atomistic calculations of rea l-sized NPG samples, based on seamlessly integrated density functional theory and tight-binding regions. We link the origins of this interference phenomenon to the band structure of the NPG. Most importantly, we demonstrate how the Talbot effect may be detected experimentally using dual-probe scanning tunneling microscopy. Talbot interference of electron waves in NPG or other related materials may open up new opportunities for future quantum electronics, computing or sensing.

E. Minamitani, N. Takagi, R. Arafune, T. Frederiksen, T. Komeda, H. Ueba, and S. Watanabe
Inelastic electron tunneling spectroscopy by STM of phonons at solid surfaces and interfaces
Prog. Surf. Sci. 93, 131-145 (2018) [ PDF ] [DOI]

Inelastic electron tunneling spectroscopy (IETS) combined with scanning tunneling microscopy (STM) allows the acquisition of vibrational signals at surfaces. In STM-IETS, a tunneling electron may excite a vibration, and opens an inelastic channel in parallel with the elastic one, giving rise to a change in conductivity of the STM junction. Until recently, the application of STM-IETS was limited to the localized vibrations of single atoms and molecules adsorbed on surfaces. The theory of the STM-IETS spectrum in such cases has been established. For the collective lattice dynamics, i.e., phonons, however, features of STM-IETS spectrum have not been understood well, though in principle STM-IETS should also be capable of detecting phonons. In this review, we present STM-IETS investigations for surface and interface phonons and provide a theoretical analysis. We take surface phonons on Cu(110) and interfacial phonons relevant to graphene on SiC substrate as illustrative examples. In the former, we provide a theoretical formalism about the inelastic phonon excitations by tunneling electrons based on the nonequilibrium Green's function (NEGF) technique applied to a model Hamiltonian constructed in momentum space for both electrons and phonons. In the latter case, we discuss the experimentally observed spatial dependence of the STM-IETS spectrum and link it to local excitations of interfacial phonons based on ab-initio STM-IETS simulation.

I. Martinez, J. P. Cascales, C. Gonzalez-Ruano, J. Y. Hong, C. F. Hung, M.-T. Lin, T. Frederiksen, and F. G. Aliev
Magnetic-state controlled molecular vibrational dynamics at buried molecular-metal interfaces
J. Phys. Chem. C 122, 26499-26505 (2018) [ PDF ] [DOI] [arXiv:1811.05363] [HTML5]

Self-assembled molecular (SAM) structures have been intensively used in molecular electronics and spintronics. However, detailed nature of the interfaces between molecular layers and extended metallic contacts used to bias the real devices remains unclear. Buried interfaces greatly restrict application of standard techniques such as Raman or scanning electron microscopies. Here we introduce low-frequency noise spectroscopy as a tool to characterize buried molecular-metal interfaces. We take advantage of vibrational heating of the molecules with incomplete contacts to the interface. Electrons, being the main spin and charge carriers propagating through the interfaces involving SAMs, interact inelastically with the nuclei and excite quantum molecular vibrations (phonons). Our detailed investigation of both conductance and conductance fluctuations in magnetic tunnel junctions with few nm Perylenetetracarboxylic dianhydride (PTCDA) allows to map vibrational heating at specific biases taking place in hot spots such as where SAM layers make unstable contact to the metallic electrodes. We follow this effect as a function of PTCDA thickness and find the highest molecular-metal order for the lowest (3-5 monolayers) barriers. Moreover, we show experimentally that the low-frequency noise depends on the relative alignment of the electrodes well beyond expectations from fluctuation-dissipation theorem. In combination with modeling, we interpret this effect as due to a magnetic-state dependent molecular vibrational heating at the interfaces driven by the spin-polarized current.

B. Hellsing, T. Frederiksen, F. Mazzola, T. Balasubramanian, and J. Wells
Phonon-induced linewidths of graphene electronic states
Phys. Rev. B 98, 205428 (2018) [ PDF ] [DOI] [arXiv:1808.08620] [HTML5]

The linewidths of the $\pi$ and $\sigma$ bands originating from the electron-phonon coupling in graphene are analyzed based on model calculations and experimental angle-resolved photoemission spectroscopy (ARPES) data. We find evidence for crucial contributions to the lifetime broadening from interband scattering $\pi\rightarrow\sigma$ and $\sigma\rightarrow\pi$ respectively, driven by the out-of-plane ZA acoustic phonons. The essential features of the calculated $\sigma$ band linewidths are in agreement with recent published ARPES data [F. Mazzola et al., Phys. Rev. B. 95, 075430 (2017)] and of the $\pi$ band linewidth with ARPES data presented here.

H. Okuyama, H. So, S. Hatta, T. Frederiksen, and T. Aruga
Effect of adsorbates on single-molecule junction conductance
Surface Science 678, 169-176 (2018) [ PDF ] [DOI]

Electronic conduction through molecular junctions depends critically on the electronic state at the anchor site, suggesting that local reactions on the electrodes may play an important role in determining the transport properties. However, single-molecule junctions have never been studied with the chemical states of the electrodes controlled down to the atomic scale. Here, we study the effect of surface adsorbates on the molecular junction conductance by using a scanning tunneling microscope (STM) combined with density functional theory (DFT) and nonequilibrium Green's function (NEGF) calculations. By vertical control of a STM tip over a phenoxy (PhO) molecule on Cu(110), we can lift and release the molecule against the tip, and thus reproducibly control a molecular junction. Using this model system, we investigate how the conductance changes as the molecule is brought to the vicinity of oxygen atoms or a hydroxyl group chemisorbed on the surface. This proximity effect of surface adsorbates on the molecular conductance is simulated by DFT-NEGF calculations.

B. de la Torre, M. Svec, G. Foti, O. Krejci, P. Hapala, A. Garcia-Lekue, T. Frederiksen, R. Zboril, A. Arnau, H. Vazquez, and P. Jelinek
Submolecular resolution by variation of inelastic electron tunneling spectroscopy amplitude and its relation to the AFM/STM signal
Phys. Rev. Lett. 119, 166001 (2017) [ PDF ] [DOI] [arXiv:1710.06180].

Here we show scanning tunnelling microscopy (STM), non-contact atomic force microscopy (AFM) and inelastic electron tunnelling spectroscopy (IETS) measurements on organic molecule with a CO-terminated tip at 5K. The high-resolution contrast observed simultaneously in all channels unambiguously demonstrates the common imaging mechanism in STM/AFM/IETS, related to the lateral bending of the CO-functionalized tip. The IETS spectroscopy reveals that the submolecular contrast at 5K consists of both renormalization of vibrational frequency and variation of the amplitude of IETS signal. This finding is also corroborated by first principles simulations. We extend accordingly the probe-particle AFM/STM/IETS model to include these two main ingredients necessary to reproduce the high-resolution IETS contrast. We also employ the first principles simulations to get more insight into different response of frustrated translation and rotational modes of CO-tip during imaging.

E. Minamitani, R. Arafune, T. Frederiksen, T. Suzuki, S. M. F. Shahed, T. Kobayashi, N. Endo, H. Fukidome, S. Watanabe, and T. Komeda
Atomic-scale characterization of the interfacial phonon in graphene/SiC
Phys. Rev. B 96, 155431 (2017) [ PDF ] [DOI]

Epitaxial graphene on SiC that provides wafer-scale and high-quality graphene sheets on an insulating substrate is a promising material to realize graphene-based nanodevices. The presence of the insulating substrate changes the physical properties of free-standing graphene through the interfacial phonon, e.g., limiting the mobility. Despite such known impacts on the material properties, a complete and microscopic picture is missing. Here we report on atomically resolved inelastic electron tunneling spectroscopy (IETS) with a scanning tunneling microscope for epitaxial graphene grown on 4H-SiC(0001). Our data reveals a strong spatial dependence in the IETS spectrum which cannot be explained by intrinsic graphene properties. We show that this variation in the IETS spectrum originates from a localized low-energy vibration of the interfacial Si atom with a dangling bond via ab-initio electronic and phononic state calculations. This insight may help advancing graphene device performance through interfacial control.

T. Jasper-Tönnies, A. Garcia-Lekue, T. Frederiksen, S. Ulrich, R. Herges, and R. Berndt
Conductance of a freestanding conjugated molecular wire (Editors' suggestion )
Phys. Rev. Lett. 119, 066801 (2017) [ PDF ] [DOI]

A freestanding molecular wire is placed vertically on Au(111) using a platform molecule and contacted by a scanning tunneling microscope. Despite the simplicity of the single-molecule junction its conductance G reproducibly varies in a complex manner with the electrode separation. Transport calculations show that G is controlled by a deformation of the molecule, a symmetry mismatch between the tip and molecule orbitals, and the breaking of a C\equivC triple in favor of a Au--C--C bond. This tip-controlled reversible bond formation/rupture alters the electronic spectrum of the junction and the states accessible for transport, resulting in an order of magnitude variation of the conductance.

F. Mazzola, T. Frederiksen, T. Balasubramanian, P. Hofmann, B. Hellsing, and J. W. Wells
Strong electron-phonon coupling in the σ band in graphene
Phys. Rev. B 95, 075430 (2017) [ PDF ] [DOI] [arXiv:1607.00939].

First-principles studies of the electron-phonon coupling in graphene predict a high coupling strength for the σ band with λ values of up to 0.9. Near the top of the σ band, λ is found to be ≈ 0.7. This value is consistent with the recently observed kinks in the σ band dispersion by angle-resolved photoemission. While the photoemission intensity from the σ band is strongly influenced by matrix elements due to sub-lattice interference, these effects differ significantly for data taken in the first and neighboring Brillouin zones. This can be exploited to disentangle the influence of matrix elements and electron-phonon coupling. A rigorous analysis of the experimentally determined complex self-energy using Kramers-Kronig transformations further supports the assignment of the observed kinks to strong electron-phonon coupling and yields a coupling constant of 0.6(1), in excellent agreement with the calculations.

P. Brandimarte, M. Engelund, N. Papior, A. Garcia-Lekue, T. Frederiksen, D. Sánchez-Portal
A tunable electronic beam splitter realized with crossed graphene nanoribbons
J. Chem. Phys. 146, 092318 (2017) [ PDF ] [DOI] [arXiv:1611.03337].

Graphene nanoribbons (GNRs) are promising components in future nanoelectronics due to the large mobility of graphene electrons and their tunable electronic band gap in combination with recent experimental developments of on-surface chemistry strategies for their growth. Here we explore a prototype 4-terminal semiconducting device formed by two crossed armchair GNRs (AGNRs) using state-of-the-art first-principles transport methods. We analyze in detail the roles of intersection angle, stacking order, inter-GNR separation, and finite voltages on the transport characteristics. Interestingly, when the AGNRs intersect at θ=60˚, electrons injected from one terminal can be split into two outgoing waves with a tunable ratio around 50% and with almost negligible back-reflection. The splitted electron wave is found to propagate partly straight across the intersection region in one ribbon and partly in one direction of the other ribbon, i.e., in analogy of an optical beam splitter. Our simulations further identify realistic conditions for which this semiconducting device can act as a mechanically controllable electronic beam splitter with possible applications in carbon-based quantum electronic circuits and electron optics. We rationalize our findings with a simple model that suggests that electronic beam splitters can generally be realized with crossed GNRs.

N. Papior, N. Lorente, T. Frederiksen, A. García, and M. Brandbyge
Improvements on non-equilibrium and transport Green function techniques: the next-generation TRANSIESTA
Comput. Phys. Commun. 212, 8–24 (2017) [ PDF ] [DOI] [arXiv:1607.04464].

We present novel methods implemented within the non-equilibrium Green function code (NEGF) transiesta based on density functional theory (DFT). Our flexible, next-generation DFT-NEGF code handles devices with one or multiple electrodes (N≥1) with individual chemical potentials and electronic temperatures. We describe its novel methods for electrostatic gating, contour opti- mizations, and assertion of charge conservation, as well as the newly implemented algorithms for optimized and scalable matrix inversion, performance-critical pivoting, and hybrid parallellization. Additionally, a generic NEGF post-processing code (tbtrans/phtrans) for electron and phonon transport is presented with several novelties such as Hamiltonian interpolations, N≥1 electrode capability, bond-currents, generalized interface for user-defned tight-binding transport, transmission projection using eigenstates of a projected Hamiltonian, and fast inversion algorithms for large-scale simulations easily exceeding 106 atoms on workstation computers. The new features of both codes are demonstrated and bench-marked for relevant test systems.

A. Shiotari, H. Okuyama, S. Hatta, T. Aruga, M. Alducin, and T. Frederiksen
Role of valence states of adsorbates in inelastic electron tunneling spectroscopy: A study of nitric oxide on Cu(110) and Cu(001)
Phys. Rev. B 94, 075442 (2016) [ PDF ]

We studied nitric oxide (NO) molecules on Cu(110) and Cu(001) surfaces with low-temperature scanning tunneling microscopy (STM) and density functional theory (DFT). NO monomers on the surfaces are characterized by STM images reflecting 2π* resonance states located at the Fermi level. NO is bonded vertically to the twofold short-bridge site on Cu(110) and to the fourfold hollow site on Cu(001). When NO molecules form dimers on the surfaces the valence orbitals are modified due to the covalent bonding. We measured inelastic electron tunneling spectroscopy (IETS) for both NO monomers and dimers on the two surfaces, and detected characteristic structures assigned to frustrated rotation and translation modes by density functional theory simulations. Considering symmetries of valence orbitals and vibrational modes, we explain the intensity of the observed IETS signals in a qualitative manner.

M. Engelund, N. Papior, P. Brandimarte, T. Frederiksen, A. Garcia-Lekue, and D. Sánchez-Portal
Search for a metallic dangling-bond wire on H-passivated semiconductor surface
J. Phys. Chem. C 120, 20303–20309 (2016) [ PDF ] [arXiv:1609.03842].

We have theoretically investigated the electronic properties of neutral and n-doped dangling bond (DB) quasi-one-dimensional structures (lines) in the Si(001):H and Ge(001):H substrates with the aim of identifying atomic-scale interconnects exhibiting metallic conduction for use in on-surface circuitry. Whether neutral or doped, DB lines are prone to suffer geometrical distortions or have magnetic ground-states that render them semiconducting. However, from our study we have identified one exception – a dimer row fully stripped of hydrogen passivation. Such a DB-dimer line shows an electronic band structure which is remarkably insensitive to the doping level and, thus, it is possible to manipulate the position of the Fermi level, moving it away from the gap. Transport calculations demonstrate that the metallic conduction in the DB-dimer line can survive thermally induced disorder, but is more sensitive to imperfect patterning. In conclusion, the DB-dimer line shows remarkable stability to doping and could serve as a one-dimensional metallic conductor on n-doped samples.

J. N. Ladenthin, T. Frederiksen, M. Persson, J. C. Sharp, S. Gawinkowski, J. Waluk, and T. Kumagai
Force-induced tautomerization in a single molecule
Nature Chemistry 8, 935–940 (2016) [ PDF ]

Heat transfer, electrical potential and light energy are common ways to activate chemical reactions. Applied force is another way, but dedicated studies for such a mechanical activation are limited, and this activation is poorly understood at the single-molecule level. Here, we report force-induced tautomerization in a single porphycene molecule on a Cu(110) surface at 5 K, which is studied by scanning probe microscopy and density functional theory calculations. Force spectroscopy quantifies the force needed to trigger tautomerization with submolecular spatial resolution. The calculations show how the reaction pathway and barrier of tautomerization are modified in the presence of a copper tip and reveal the atomistic origin of the process. Moreover, we demonstrate that a chemically inert tip whose apex is terminated by a xenon atom cannot induce the reaction because of a weak interaction with porphycene and a strong relaxation of xenon on the tip as contact to the molecule is formed.

M. Engelund, S. Godlewski, M. Kolmer, R. Zuzak, B. Such, T. Frederiksen, M. Szymonski, and D. Sánchez-Portal
The butterfly – a well-defined constant-current topography pattern on Si(001):H and Ge(001):H resulting from current-induced defect fluctuations
Phys. Chem. Chem. Phys. 18, 19309 (2016) [ PDF ]

Dangling bond (DB) arrays on Si(001):H and Ge(001):H surfaces can be patterned with atomic precision and they exhibit complex and rich physics making them interesting from both technological and fundamental perspectives. But their complex behavior often makes scanning tunneling microscopy (STM) images difficult to interpret and simulate. Recently it was shown that low-temperature imaging of unoccupied states of an unpassivated dimer on Ge(001):H results in a symmetric butterfly-like STM pattern, despite that the equilibrium dimer configuration is expected to be a bistable, buckled geometry. Here, based on a thorough characterization of the low-bias switching events, we propose a new imaging model featuring a dynamical two-state rate equation. This model allows us to reproduce the features of the observed symmetric empty-state images which strongly corroborates the idea that the patterns arise due to fast switching events and provides insight into the relation between the tunneling current and switching rates. Our new imaging model is general and can be applied to other systems that exhibit rapid fluctuations during STM experiments.

Y. Kitaguchi, S. Habuka, H. Okuyama, S. Hatta, T. Aruga, T. Frederiksen, M. Paulsson, and H. Ueba
Controlled switching of single-molecule junctions by mechanical motion of a phenyl ring
Beilstein J. Nanotechnol. 6, 2088-2095 (2015) [ PDF ]

Mechanical methods for single-molecule control have potential for wide application in nanodevices and machines. Here we demonstrate the operation of a single-molecule switch made functional by the motion of a phenyl ring, analogous to the lever in a conventional toggle switch. The switch can be actuated by dual triggers, either by a voltage pulse or by displacement of the electrode, and electronic manipulation of the ring by chemical substitution enables rational control of the on-state conductance. Owing to its simple mechanics, structural robustness, and chemical accessibility, we propose that phenyl rings are promising components in mechanical molecular devices.

M. Engelund, R. Zuzak, S. Godlewski, M. Kolmer, T. Frederiksen, A. García-Lekue, D. Sánchez-Portal, and M. Szymonski
Tunneling spectroscopy of close-spaced dangling-bond pairs in Si(001):H
Scientific Reports 5, 14496 (2015) [ PDF ]

We present a combined experimental and theoretical study of the electronic properties of close- spaced dangling-bond (DB) pairs in a hydrogen-passivated Si(001):H p-doped surface. Two types of DB pairs are considered, called "cross" and "line" structures. Our scanning tunneling spectroscopy (STS) data show that, although the spectra taken over different DBs in each pair exhibit a remarkable resemblance, they appear shifted by a constant energy that depends on the DB-pair type. This spontaneous asymmetry persists after repeated STS measurements. By comparison with density functional theory (DFT) calculations, we demonstrate that the magnitude of this shift and the relative position of the STS peaks can be explained by distinct charge states for each DB in the pair. We also explain how the charge state is modified by the presence of the scanning tunneling microscopy (STM) tip and the applied bias. Our results indicate that, using the STM tip, it is possible to control the charge state of individual DBs in complex structures, even if they are in close proximity. This observation might have important consequences for the design of electronic circuits and logic gates based on DBs in passivated silicon surfaces.

T. Frederiksen
First-principles simulations of electron transport in atomic-scale systems
Book chapter for Handbook of Single-Molecule Electronics edited by K. Moth-Poulsen, Pan Stanford (2015).

An important theoretical challenge in the field of single-molecule electronics is to develop general methods for quantitative simulations of real devices taking into account the atomistic details. This chapter describes an approach toward this goal based on density-functional theory (DFT) for the electronic structure in combination with nonequilibrium Green's functions (NEGF) for the transport. We also address recent developments based on the DFT+NEGF approach to describe electron--vibration interactions in molecular junctions, local heating effects, and inelastic signatures in device current--voltage and shot noise characteristics.

Y. Kitaguchi, S. Habuka, H. Okuyama, S. Hatta, T. Aruga, T. Frederiksen, M. Paulsson, and H. Ueba
Controlling single-molecule junction conductance by molecular interactions
Scientific Reports 5, 11796 (2015) [ PDF ]

For the rational design of single-molecular electronic devices, it is essential to understand environmental effects on the electronic properties of a working molecule. Here we investigate the impact of molecular interactions on the single-molecule conductance by accurately positioning individual molecules on the electrode. To achieve reproducible and precise conductivity measurements, we utilize relatively weak π-bonding between a phenoxy molecule and a STM-tip to form and cleave one contact to the molecule. The anchoring to the other electrode is kept stable using a chalcogen atom with strong bonding to a Cu(110) substrate. These non-destructive measurements permit us to investigate the variation in single-molecule conductance under different but controlled environmental conditions. Combined with density functional theory calculations, we clarify the role of the electrostatic field in the environmental effect that influences the molecular level alignment.

R. B. Christensen, T. Frederiksen, and M. Brandbyge
Identification of pristine and defective graphene nanoribbons by phonon signatures in the electron transport characteristics
Phys. Rev. B 91, 075434 (2015) [ PDF ] [arXiv:1501.02266]

Inspired by recent experiments where electron transport was measured across graphene nanoribbons (GNRs) suspended between a metal surface and the tip of a scanning tunneling microscope [Koch et al., Nat. Nanotechnol. 7, 713 (2012)], we present detailed first-principles simulations of inelastic electron tunneling spectroscopy (IETS) of long pristine and defective armchair and zigzag nanoribbons under a range of charge carrier conditions. For the armchair ribbons we find two robust IETS signals around 169 and 196 mV corresponding to the D and G modes of Raman spectroscopy as well as additional fingerprints due to various types of defects in the edge passivation. For the zigzag ribbons we show that the spin state strongly influences the spectrum and thus propose IETS as an indirect proof of spin polarization.

G. Foti, D. Sánchez-Portal, A. Arnau, and T. Frederiksen
Role of k-point sampling in the supercell approach to inelastic electron tunneling spectroscopy simulations of molecular monolayers
Phys. Rev. B 91, 035434 (2015) [ PDF ]

While the role of sampling of the electron momentum k in supercell calculations of the elastic electron transmission is well understood, its influence in the case of inelastic electron tunneling (IET) has not yet been systematically explored. Here we compare ab initio IET spectra of molecular monolayers in the commonly used Γ-point approximation to rigorously k-converged results. We study four idealized molecular junctions with either alkanedithiolates or benzenedithiolates, and explore variations due to varying molecular tilt angle, density, as well as chemical identity of the monolayer. We show that the Γ-point approximation is reasonable for a range of systems, but that a rigorous convergence is needed for accurate signal amplitudes. We also describe an approximative scheme which reduces the computational cost of the k-averaged calculation in our implementation.

Y. Kim, K. Motobayashi, T. Frederiksen, H. Ueba, and M. Kawai
Action spectroscopy for single-molecules reactions - experiment and theory
Prog. Surf. Sci. 90, 85-143 (2015) [ PDF ] [DOI]

We review several representative experimental results of action spectroscopy (AS) of single molecules on metal surfaces using a scanning tunneling microscope (STM) by M. Kawai's group over last decade. The experimental procedures to observe STM-AS are described. A brief description of a low-temperature STM and experimental setup are followed by key experimental techniques of how to determine an onset bias voltage of a reaction and how to measure a current change associated with reactions and finally how to observe AS for single molecule reactions. The experimental results are presented for vibrationally mediated chemical transformation of trans-2-butene to 1.3-butadiene molecule and rotational motion of a single cis-2-butene molecule among four equivalent orientations on Pd(110). The AS obtained from the motion clearly detects more vibrational modes than inelastic electron tunneling spectroscopy with an STM. AS is demonstrated as a useful and novel single molecule vibrational spectroscopy. The AS for a lateral hopping of water dimer on Pt(111) is presented as an example of novelty. Several distinct vibrational modes are detected as the thresholds in the AS. The assignment of the vibrational modes determined from the analysis of the AS is made from a view of the adsorption geometry of hydrogen-bond donor or acceptor molecules in water dimer.

A generic theory of STM-AS, i.e., a reaction rate or yield as a function of bias voltage, is presented using a single adsorbate resonance model for single molecule reactions induced by the inelastic tunneling current. Formulas for the reaction rate R(V) and Y(V), i.e., reaction yield per electron Y(V) = e R(V)/I are derived. It provides a versatile framework to analyze any vibrationally mediated reactions of single adsorbates on metal surfaces. Numerical examples are presented to demonstrate generic features of the vibrational generation rate and Y(V) at different levels of approximations and to show how the effective broadening of the vibrational density of states (as described by Gaussian or Lorentzian functions) manifest themselves in Y(V) near the threshold bias voltage corresponding to a vibrational excitation responsible for reactions. A prefactor of Y(V) is explicitly derived for various types of elementary processes. Our generic formula of Y(V) also underlines the need to observe Y(V) at both bias voltage polarities, which can provide additional insight into the adsorbate projected density of states near the Fermi level within a span of the vibrational energy.

The theory is applied to analysis of some highlights of the experimental results: Xe transfer, hopping of a single CO molecule on Pd(110), a dissociation of a single dimethyl disulfide (CH3S)2 and a hopping of a dissociated product, i.e., single methyl thiolate CH3S on Cu(111). It underlines that an observation of Y(V) at both bias polarities permits us to certain insight into the molecular alignment with respect to the Fermi level.

K. Smaali, S. Desbief, G. Foti, T. Frederiksen, D. Sánchez-Portal, A. Arnau, J.-P. Nys, P. Leclere, D. Vuillaume, and N. Clement
On the mechanical and electronic properties of thiolated gold nanocrystals
Nanoscale 7, 1809-1819 (2015) [ PDF ] [ Suppl. ] [arXiv:1412.7698]
Selected as "Hot article"

We present a quantitative exploration, combining experiment and simulation, of the mechanical and electronic properties, as well as the modifications induced by an alkylthiolated coating, at the single nanoparticle (NP) level. We determined the response of the NPs to external pressure in a controlled manner using an atomic force microscope tip. We found a strong reduction in their Young's modulus, as compared to bulk gold, and a significant influence of strain on the electronic properties of the alkylthiolated NPs. Electron transport measurements of tiny molecular junctions (NP/alkylthiol/CAFM tip) show that the effective tunnelling barrier through the adsorbed monolayer strongly decreases by increasing the applied load, which translates in a remarkable and unprecedented increase in the tunnel current. These observations are successfully explained using simulations based on the finite element analysis (FEA) and first-principles calculations that permit one to consider the coupling between the mechanical response of the system and the electric dipole variations at the interface.

G. Foti, H. Vázquez, D. Sánchez-Portal, A. Arnau, and T. Frederiksen
Identifying highly-conducting Au-C links through inelastic electron tunneling spectroscopy
J. Phys. Chem. C 118, 27106-27112 (2014) [ PDF ]

We use inelastic electron tunneling spectroscopy first-principles simulations to identify the different chemical bonds present at metal-molecule junctions. We unambiguously identify the nature of these bonds from two distinctive features in the calculated spectra: (i) the presence (or absence) of active vibrational modes and (ii) the dependence of vibrational frequencies on electrode separation. We use this method to present a study of the vibrational properties of alkanes bound to the electrodes via highly conducting Au-C links. In the experiment, these links were formed from molecules synthesized with trimethyl-tin (SnMe3) terminations, where the SnMe3 groups were removed in situ at the junction, in a process involving both breaking and formation of bonds [Cheng, Z.-L.; Skouta, R.; Vázquez, H.; Widawsky, J. R.; Schneebeli, S.; Chen, W.; Hybertsen, M. S.; Breslow, R.; Venkataraman, L. Nat. Nanotechnol. 2011, 6, 353-357]. We obtain the vibrational fingerprint of these direct Au-alkane links and extend this study to the other scenario considered in that paper (bonding via SnMe2 groups), which may be relevant under other experimental conditions. We also explore the effect of deuteration on inelastic electron tunneling spectroscopy (IETS). Complete deuteration of the molecules diminishes the differences of the spectra corresponding to the two bonding geometries, making identification more difficult. IETS of an isolated SnMe3 fragment provides an additional basis for comparison in the characterization of the molecular junction.

T. Frederiksen, G. Foti, F. Scheurer, V. Speisser, and G. Schull
Chemical control of electrical contacts to sp2 carbon atoms
Nat. Commun. 5, 3659 (2014) [ PDF ]

Carbon-based nanostructures are attracting tremendous interest as components in ultrafast electronics and optoelectronics. The electrical interfaces to these structures play a crucial role for the electron transport, but the lack of control at the atomic scale can hamper device functionality and integration into operating circuitry. Here we study a prototype carbon-based molecular junction consisting of a single C60 molecule and probe how the electric current through the junction depends on the chemical nature of the foremost electrode atom in contact with the molecule. We find that the efficiency of charge injection to a C60 molecule varies substantially for the considered metallic species, and demonstrate that the relative strength of the metal-C bond can be extracted from our transport measurements. Our study further suggests that a single-C60 junction is a basic model to explore the properties of electrical contacts to meso- and macroscopic sp2 carbon structures.

J.-T. Lü, R. B. Christensen, G. Foti, T. Frederiksen, T. Gunst, and M. Brandbyge
Efficient calculation of inelastic vibration signals in electron transport: Beyond the wide-band approximation
Phys. Rev. B 89, 081405(R) (2014) [ PDF ] [arXiv:1312.7625].

We extend the simple and efficient lowest order expansion (LOE) for inelastic electron tunneling spectroscopy (IETS) to include variations in the electronic structure on the scale of the vibration energies. This enables first-principles calculations of IETS line shapes for molecular junctions close to resonances and band edges. We demonstrate how this is relevant for the interpretation of experimental IETS using both a simple model and first-principles simulations.

T. Frederiksen, M. Paulsson, and H. Ueba
Theory of action spectroscopy for single-molecule reactions induced by vibrational excitations with STM
Phys. Rev. B 89, 035427 (2014) [ PDF ]

A theory of action spectroscopy, i.e., a reaction rate or yield as a function of bias voltage, is presented for single-molecule reactions induced by the inelastic tunneling current with a scanning tunneling microscope. A formula for the reaction yield is derived using the adsorbate resonance model, which provides a versatile tool to analyze vibrationally mediated reactions of single adsorbates on conductive surfaces. This allows us to determine the energy quantum of the excited vibrational mode, the effective broadening of the vibrational density of states (as described by Gaussian or Lorentzian functions), and a prefactor characterizing the elementary process behind the reaction. The underlying approximations are critically discussed. We point out that observation of reaction yields at both bias voltage polarities can provide additional insight into the adsorbate density of states near the Fermi level. As an example, we apply the theory to the case of flip motion of a hydroxyl dimer (OD)2 on Cu(110) which was experimentally observed by Kumagai et al. [Phys. Rev. B 79, 035423 (2009)]. In combination with density functional theory calculations for the vibrational modes, the vibrational damping due to electron-hole pair generation, and the potential energy landscape for the flip motion, a detailed microscopic picture for the switching process is established. This picture reveals that the predominant mechanism is excitation of the OD stretch modes which couple anharmonically to the low-energy frustrated rotation mode.

G. Foti, D. Sánchez-Portal, A. Arnau, and T. Frederiksen
Interface dipole effects as a function of molecular tilt: mechanical gating of electron tunneling through self-assembled monolayers?
J. Phys. Chem. C 117, 14272-14280 (2013) [ PDF ]

Control of electron transport through molecular devices is a fundamental step toward design of functional molecular electronics. In this respect, the application of the field-effect transistor principle to molecular junctions appears to be a desirable strategy. Here we study the possibility of mechanically controlling the molecular orbital alignment in self-assembled monolayers via the electrostatic fields originating from dipoles at the metal-molecule interfaces. More specifically, we analyze first-principles simulations of prototype alkanedithiolate and alkanediamine monolayer junctions between Au(111) electrodes as a function of inclination of the molecules in the film. We find that the molecular orbital alignment and hence the low-bias conductance of the junctions, sensitively depends on the interface dipole. The dipole change with molecular tilt is rationalized in terms of two electrostatic effects: (i) the reorientation of a dipole associated with the anchoring group and (ii) a dipole modification arising from charge redistribution due to the metal-molecule bond. The first effect, dominating for the thiolates, is the desired way to gate the junctions by tuning of the molecular tilt. However, the second effect, equally important for the amines, may hamper the mechanical control of the level alignment because it depends on other geometric details than the tilt angle. Our results thus suggest that mechanical gating by tilt is achievable with molecules and anchoring groups with strong intrinsic dipole moments and well-defined binding geometry rather than with interface dipoles associated with weak and flexible metal-molecule bonds.

S. Ulstrup, T. Frederiksen, and M. Brandbyge,
Nonequilibrium electron-vibration coupling and conductance fluctuations in a C60-junction
Phys. Rev. B 86, 245417 (2012) [ PDF ] [arXiv:1209.5644]

We investigate chemical bond formation and conductance in a molecular C60 junction under finite bias voltage using first-principles calculations based on density functional theory and nonequilibrium Green's functions (DFT-NEGF). At the point of contact formation we identify a remarkably strong coupling between the C60 motion and the molecular electronic structure. This is only seen for positive sample bias, although the conductance itself is not strongly polarity dependent. The nonequilibrium effect is traced back to a sudden shift in the position of the voltage drop with a small C60 displacement. Combined with a vibrational heating mechanism we construct a model from our results that explain the polarity-dependent two-level conductance fluctuations observed in recent scanning tunneling microscopy (STM) experiments [N. Néel et al., Nano Lett. 11, 3593 (2011)]. These findings highlight the significance of nonequilibrium effects in chemical bond formation/breaking and in electron-vibration coupling in molecular electronics.

Y. Kim, A. Garcia-Lekue, D. Sysoiev, T. Frederiksen, U. Groth, and E. Scheer,
Charge transport in azobenzene-based single-molecule junctions
Phys. Rev. Lett. 109, 226801 (2012) [ PDF ] [ Suppl. ]

Azobenzene-derivative molecules change their conformation as a result of a cis-trans transition when exposed to ultraviolet or visible light irradiation and this is expected to induce a significant variation in the conductance of molecular devices. Despite extensive investigations carried out on this type of molecule, a detailed understanding of the charge transport for the two isomers is still lacking. We report a combined experimental and theoretical analysis of electron transport through azobenzene-derivative single-molecule break junctions with Au electrodes. Current-voltage and inelastic electron tunneling spectroscopy (IETS) measurements performed at 4.2 K are interpreted based on first-principles calculations of electron transmission and IETS spectra. This qualitative study unravels the origin of a slightly higher conductance of junctions with the cis isomer and demonstrates that IETS spectra of cis and trans forms show distinct vibrational fingerprints that can be used for identifying the isomer.

R. Avriller, and T. Frederiksen,
Inelastic shot noise characteristics of nanoscale junctions from first principles
Phys. Rev. B 86, 155411 (2012) [ PDF ] [arXiv:1209.3599]

We describe an implementation of ab initio methodology to compute inelastic shot noise signals due to electron-vibration scattering in nanoscale junctions. The method is based on the framework of nonequilibrium Keldysh Green's functions with a description of electronic structure and nuclear vibrations from density functional theory. Our implementation is illustrated with simulations of electron transport in Au and Pt atomic point contacts. We show that the computed shot noise characteristics of the Au contacts can be understood in terms of a simple two-site tight-binding model representing the two apex atoms of the vibrating nanojunction. We also show that the shot noise characteristics of Pt contacts exhibit more complex features associated with inelastic interchannel scattering. These inelastic noise features are shown to provide additional information about the electron-phonon coupling and the multichannel structure of Pt contacts than what is readily derived from the corresponding conductance characteristics. We finally analyze a set of Au atomic chains of different lengths and strain conditions and provide a quantitative comparison with the recent shot noise experiments reported by Kumar et al. [Phys. Rev. Lett. 108, 146602 (2012)].

N. Hauptmann, F. Mohn, L. Gross, G. Meyer, T. Frederiksen, and R. Berndt,
Force and conductance during contact formation to a C60 molecule
New J. Phys. 14, 073032 (2012) [ PDF ] [ Suppl. ] [arXiv:1208.2791]

Force and conductance were simultaneously measured during the formation of Cu-C60 and C60-C60 contacts using a combined cryogenic scanning tunneling and atomic force microscope. The contact geometry was controlled with submolecular resolution. The maximal attractive forces measured for the two types of junctions were found to differ significantly. We show that the previously reported values of the contact conductance correspond to the junction being under maximal tensile stress.

T. Kumagai, A. Shiotari, H. Okuyama, S. Hatta, T. Aruga, I. Hamada, T. Frederiksen, and H. Ueba,
H-atom relay reactions in real space
Nature Materials 11, 167-172 (2012) [ PDF ] [ Suppl. ]

Hydrogen bonds are the path through which protons and hydrogen atoms can be transferred between molecules. The relay mechanism, in which H-atom transfer occurs in a sequential fashion along hydrogen bonds, plays an essential role in many functional compounds. Here we use the scanning tunnelling microscope to construct and operate a test-bed for real-space observation of H-atom relay reactions at a single-molecule level. We demonstrate that the transfer of H-atoms along hydrogen-bonded chains assembled on a Cu(110) surface is controllable and reversible, and is triggered by excitation of molecular vibrations induced by inelastic tunnelling electrons. The experimental findings are rationalized by ab initio calculations for adsorption geometry, active vibrational modes and reaction pathway, to reach a detailed microscopic picture of the elementary processes.

B. W. Heinrich, M. V. Rastei, D.- J. Choi, T. Frederiksen, and L. Limot,
Engineering negative differential conductance with the Cu(111) surface state
Phys. Rev. Lett. 107, 246801 (2011) [ PDF ] [arXiv:1112:1801v1].

Low-temperature scanning tunneling microscopy and spectroscopy are employed to investigate electron tunneling from a C60-terminated tip into a Cu(111) surface. Tunneling between a C60 orbital and the Shockley surface states of copper is shown to produce negative differential conductance (NDC) contrary to conventional expectations. NDC can be tuned through barrier thickness or C60 orientation up to complete extinction. The orientation dependence of NDC is a result of a symmetry matching between the molecular tip and the surface states.

Y. Ootsuka, T. Frederiksen, H. Ueba, and M. Paulsson,
Vibrationally induced flip motion of a hydroxyl dimer on Cu(110)
Phys. Rev. B 84, 193403 (2011) [ PDF ] [arXiv:1111.2252v1]

Recent low-temperature scanning-tunneling microscopy experiments [T. Kumagai et al., Phys. Rev. B 79, 035423 (2009)] observed the vibrationally induced flip motion of a hydroxyl dimer (OD)2 on Cu(110). We propose a model to describe two-level fluctuations and current-voltage characteristics of nanoscale systems that undergo vibrationally induced switching. The parameters of the model are based on comprehensive density functional calculations of the system's vibrational properties. For the dimer (OD)2, the calculated population of the high- and low-conductance states, the I-V, dI/dV, and d2I/dV2 curves are in good agreement with the experimental results and underline the different roles played by the free and shared OD stretch modes of the dimer.

A. Garcia-Lekue, D. Sánchez-Portal, A. Arnau, and T. Frederiksen,
Simulation of inelastic electron tunneling spectroscopy of single molecules with functionalized tips
Phys. Rev. B 83, 155417 (2011) [ PDF ] [arXiv:1103.4302v1]

The role of the tip in inelastic electron tunneling spectroscopy (IETS) performed with scanning tunneling microscopes (STM) is theoretically addressed via first-principles simulations of vibrational spectra of single carbon monoxide (CO) molecules adsorbed on Cu(111). We show how chemically functionalized STM tips modify the IETS intensity corresponding to adsorbate modes on the sample side. The underlying propensity rules are explained using symmetry considerations for both the vibrational modes and the molecular orbitals of the tip and sample. This suggests that single-molecule IETS can be optimized by selecting the appropriate tip orbital symmetry.

G. Schull, T. Frederiksen, A. Arnau, D. Sánchez-Portal, and R. Berndt,
Atomic-scale engineering of electrodes for single-molecule contacts
Nature Nanotechnology 6, 23-27 (2011) [ PDF ] [ Suppl. ]

The transport of charge through a conducting material depends on the intrinsic ability of the material to conduct current and on the charge injection efficiency at the contacts between the conductor and the electrodes carrying current to and from the material. According to theoretical considerations, this concept remains valid down to the limit of single-molecule junctions. Exploring this limit in experiments requires atomic-scale control of the junction geometry. Here we present a method for probing the current through a single C60 molecule while changing, one by one, the number of atoms in the electrode that are in contact with the molecule. We show quantitatively that the contact geometry has a strong influence on the conductance. We also find a crossover from a regime in which the conductance is limited by charge injection at the contact to a regime in which the conductance is limited by scattering at the molecule. Thus, the concepts of 'good' and 'bad' contacts, commonly used in macro- and mesoscopic physics, can also be applied at the molecular scale.

M. Paulsson, T. Frederiksen, and M. Brandbyge
Molecular electronics: insight from first-principles transport simulations
CHIMIA 64, 350-355 (2010) [ PDF ]

Conduction properties of nanoscale contacts can be studied using first-principles simulations. Such calculations give insight into details behind the conductance that is not readily available in experiments. For example, we may learn how the bonding conditions of a molecule to the electrodes affect the electronic transport. Here we describe key computational ingredients and discuss these in relation to simulations for scanning tunneling microscopy (STM) experiments with C60 molecules where the experimental geometry is well characterized. We then show how molecular dynamics simulations may be combined with transport calculations to study more irregular situations, such as the evolution of a nanoscale contact with the mechanically controllable break-junction technique. Finally we discuss calculations of inelastic electron tunnelling spectroscopy as a characterization technique that reveals information about the atomic arrangement and transport channels.

M. Brandbyge, T. Frederiksen, and M. Paulsson
DFT-NEGF approach to current-induced forces, vibrational signals, and heating in nanoconductors
Book chapter in T. Seideman Ed. Current-Driven Phenomena in Nanoelectronics.

In this chapter we first introduce the DFT-NEGF method, which combines density functional theory (DFT) with the nonequilibrium Green's function (NEGF) method in order to treat atomic-scale conductors in the presence of current. We introduce the concept of conductance eigenchannels within DFT-NEGF as a means of analysis of the elastic conduction process. We then describe how the inelastic processes involving interaction with vibrations can be calculated efficiently using DFT-NEGF and further approximations. We show how these methods can be used to investigate how the electronic current can heat the vibrations in the atomic-scale conductors and conclude with a discussion of some current experiments in which this is observed.

L. Vitali, R. Ohmann, K. Kern, A. Garcia-Lekue, T. Frederiksen, D. Sánchez-Portal, and A. Arnau
Surveying molecular vibrations during the formation of metal-molecule nanocontacts
Nano Lett. 10, 657-660 (2010) [ PDF ]

Molecular junctions have been characterized to determine the influence of the metal contact formation in the electron transport process through a single molecule. With inelastic electron tunneling spectroscopy and first-principles calculations, the vibration modes of a carbon monoxide molecule have been surveyed as a function of the distance from a copper electrode with unprecedented accuracy. We observe a continuous but nonlinear blue shift of the frustrated rotation mode in tunneling with decreasing distance followed by an abrupt softening upon contact formation. This indicates that the presence of the metal electrode sensibly alters the structural and conductive properties of the junction even without the formation of a strong chemical bond.

C. R. Arroyo, T. Frederiksen, G. Rubio-Bollinger, M. Vélez, A. Arnau, D. Sánchez-Portal, and N. Agraït
Characterization of single-molecule pentanedithiol junctions by inelastic electron tunneling spectroscopy and first-principles calculations
Phys. Rev. B 81, 075405 (2010) [ PDF ] [arXiv:1001.2392v1]

We study pentanedithiol molecular junctions formed by means of the break-junction technique with a scanning tunneling microscope at low temperatures. Using inelastic electron tunneling spectroscopy and first-principles calculations, the response of the junction to elastic deformation is examined. We show that this procedure makes a detailed characterization of the molecular junction possible. In particular, our results indicate that tunneling takes place through just a single molecule.

G. Schull, T. Frederiksen, M. Brandbyge, and R. Berndt
Passing current through touching molecules (Editors' suggestion )
Phys. Rev. Lett. 103, 206803 (2009) [PRL Cover] [ PDF ] [arXiv:0910:1281]
Featured in Physics Focus story: Molecular currents

The charge flow from a single C60 molecule to another one has been probed. The conformation and electronic states of both molecules on the contacting electrodes have been characterized using a cryogenic scanning tunneling microscope. While the contact conductance of a single molecule between two Cu electrodes can vary up to a factor of 3 depending on electrode geometry, the conductance of the C60-C60 contact is consistently lower by 2 orders of magnitude. First-principles transport calculations reproduce the experimental results, allow a determination of the actual C60-C60 distances, and identify the essential role of the intermolecular link in bi- and trimolecular chains.

T. Frederiksen, C. Munuera, C. Ocal, M. Brandbyge, M. Paulsson, D. Sánchez-Portal, and A. Arnau
Exploring the tilt-angle dependence of electron tunneling across molecular junctions of self-sssembled alkanethiols
ACS Nano 3, 2073-2080 (2009) [ PDF ]

Electronic transport mechanisms in molecular junctions are investigated by a combination of first-principles calculations and current-voltage measurements of several well-characterized structures. We study self-assembled layers of alkanethiols grown on Au(111) and form tunnel junctions by contacting the molecular layers with the tip of a conductive force microscope. Measurements done under low-load conditions permit us to obtain reliable tilt-angle and molecular length dependencies of the low-bias conductance through the alkanethiol layers. The observed dependence on tilt-angle is stronger for the longer molecular chains. Our calculations confirm the observed trends and explain them as a result of two mechanisms, namely, a previously proposed intermolecular tunneling enhancement as well as a hitherto overlooked tilt-dependent molecular gate effect.

M. Paulsson, C. Krag, T. Frederiksen, and M. Brandbyge
Conductance of alkanedithiol single-molecule junctions: a molecular dynamics study
Nano Lett. 9, 117-121 (2009) [ PDF ]

We study formation and conductance of alkanedithiol junctions using density functional based molecular dynamics. The formation involves straightening of the molecule, migration of thiol end-groups, and pulling out Au atoms. Plateaus are found in the low-bias conductance traces which decrease by 1 order of magnitude when gauche defects are present. We further show that the inelastic electron tunneling spectra depend on the junction geometry. In particular, our simulations suggest ways to identify gauche defects.

T. Frederiksen, K. Franke, A. Arnau, G. Schulze, J. I. Pascual, and N. Lorente
Dynamic Jahn-Teller effect in electron transport through single C60 molecules
Phys. Rev. B 78, 233401 (2008) [ PDF ] [arXiv:0804.3415]

Low-temperature scanning tunneling spectroscopy and first-principles calculations are used to characterize electron transport through vibronic states of C60 molecules. This is achieved by positioning a C60 molecule on top of a molecular self-assembled template on Au(111). In these conditions, conductance spectra are shown to reveal the dynamic Jahn-Teller effect of the C60 molecule. This vibronic transport study helps in solving a long-standing debate [Phys. Rev. Lett. 74, 1875 (1995); Phys. Rev. Lett. 91, 196402 (2003)] on density-functional calculations of the C60 electron-phonon coupling strength.

E. J. McEniry, T. Frederiksen, T. N. Todorov, D. Dundas, and A. P. Horsfield
Inelastic quantum transport in nanostructures: the self-consistent Born approximation and correlated electron-ion dynamics
Phys. Rev. B 78, 035446 (2008) [ PDF ] [arXiv:0802.4174]

A dynamical method for inelastic transport simulations in nanostructures is compared to a steady-state method based on nonequilibrium Green's functions. A simplified form of the dynamical method produces, in the steady state in the weak-coupling limit, effective self-energies analogous to those in the Born approximation due to electron-phonon coupling. The two methods are then compared numerically on a resonant system consisting of a linear trimer weakly embedded between metal electrodes. This system exhibits an enhanced heating at high biases and long phonon equilibration times. Despite the differences in their formulation, the static and dynamical methods capture local current-induced heating and inelastic corrections to the current with good agreement over a wide range of conditions, except in the limit of very high vibrational excitations where differences begin to emerge.

M. Paulsson, T. Frederiksen, H. Ueba, N. Lorente, and M. Brandbyge
Unified description of inelastic propensity rules for electron transport through nanoscale junctions
Phys. Rev. Lett. 100, 226604 (2008) [ PDF ] [arXiv:0711.3392]

We present a method to analyze the results of first-principles based calculations of electronic currents including inelastic electron-phonon effects. This method allows us to determine the electronic and vibrational symmetries in play, and hence to obtain the so-called propensity rules for the studied systems. We show that only a few scattering states - namely those belonging to the most transmitting eigenchannels - need to be considered for a complete description of the electron transport. We apply the method on first-principles calculations of four different systems and obtain the propensity rules in each case.

T. Frederiksen, N. Lorente, M. Paulsson, and M. Brandbyge
From tunneling to contact: inelastic signals in an atomic gold junction from first principles
Phys. Rev. B 75, 235441 (2007) [ PDF ] [cond-mat/0702176]

The evolution of electron conductance in the presence of inelastic effects is studied as an atomic gold contact is formed evolving from a low-conductance regime (tunneling) to a high-conductance regime (contact). In order to characterize each regime, we perform density-functional theory (DFT) calculations to study the geometric and electronic structures, together with the strength of the atomic bonds and the associated vibrational frequencies. The conductance is calculated by, first, evaluating the transmission of electrons through the system and, second, by calculating the conductance change due to the excitation of vibrations. As found in previous studies [Paulsson et al., Phys. Rev. B 72, 201101(R) (2005)], the change in conductance due to inelastic effects permits us to characterize the crossover from tunneling to contact. The most notorious effect is the crossover from an increase in conductance in the tunneling regime to a decrease in conductance in the contact regime when the bias voltage matches a vibrational threshold. Our DFT-based calculations actually show that the effect of vibrational modes in electron conductance is rather complex, in particular, when modes localized in the contact region are permitted to extend into the electrodes. As an example, we find that certain modes can give rise to decreases in conductance when in the tunneling regime, opposite to the above-mentioned result. Whereas details in the inelastic spectrum depend on the size of the vibrational region, we show that the overall change in conductance is quantitatively well approximated by the simplest calculation where only the apex atoms are allowed to vibrate. Our study is completed by the application of a simplified model where the relevant parameters are obtained from the above DFT-based calculations.

T. Frederiksen, M. Paulsson, M. Brandbyge, and A.-P. Jauho
Inelastic transport theory from first principles: methodology and application to nanoscale devices
Phys. Rev. B 75, 205413 (2007) [ PDF ] [cond-mat/0611562]

We describe a first-principles method for calculating electronic structure, vibrational modes and frequencies, electron-phonon couplings, and inelastic electron transport properties of an atomic-scale device bridging two metallic contacts under nonequilibrium conditions. The method extends the density-functional codes SIESTA and TRANSIESTA that use atomic basis sets. The inelastic conductance characteristics are calculated using the nonequilibrium Green's function formalism, and the electron-phonon interaction is addressed with perturbation theory up to the level of the self-consistent Born approximation. While these calculations often are computationally demanding, we show how they can be approximated by a simple and efficient lowest order expansion. Our method also addresses effects of energy dissipation and local heating of the junction via detailed calculations of the power flow. We demonstrate the developed procedures by considering inelastic transport through atomic gold wires of various lengths, thereby extending the results presented in Frederiksen et al. [Phys. Rev. Lett. 93, 256601 (2004)]. To illustrate that the method applies more generally to molecular devices, we also calculate the inelastic current through different hydrocarbon molecules between gold electrodes. Both for the wires and the molecules our theory is in quantitative agreement with experiments, and characterizes the system-specific mode selectivity and local heating.

T. Frederiksen, M. Paulsson, M. Brandbyge, and A.-P. Jauho
First-principles theory of inelastic transport and local heating in atomic gold wires
AIP Conf. Proc. 893, 727-728 (2007) [ PDF ]

We present theoretical calculations of the inelastic transport properties in atomic gold wires. Our method is based on a combination of density functional theory and nonequilibrium Green's functions. The vibrational spectra for extensive series of wire geometries have been calculated using SIESTA, and the corresponding effects in the conductance are analyzed. In particular, we focus on the heating of the active vibrational modes. By a detailed comparison with experiments we are able to estimate an order of magnitude for the external damping of the active vibrations.

T. Frederiksen, M. Paulsson, and M. Brandbyge
Inelastic fingerprints of hydrogen contamination in atomic gold wire systems
J. Phys.: Conf. Ser. 61, 312-316 (2007) [ PDF ] [cond-mat/0608510]

We present series of first-principles calculations for both pure and hydrogen contaminated gold wire systems in order to investigate how such impurities can be detected. We show how a single H atom or a single H2 molecule in an atomic gold wire will affect forces and Au-Au atom distances under elongation. We further determine the corresponding evolution of the low-bias conductance as well as the inelastic contributions from vibrations. Our results indicate that the conductance of gold wires is only slightly reduced from the conductance quantum G0 = 2e2/h by the presence of a single hydrogen impurity, hence making it difficult to use the conductance itself to distinguish between various configurations. On the other hand, our calculations of the inelastic signals predict significant differences between pure and hydrogen contaminated wires, and, importantly, between atomic and molecular forms of the impurity. A detailed characterization of gold wires with a hydrogen impurity should therefore be possible from the strain dependence of the inelastic signals in the conductance.

N. Néel, J. Kröger, L. Limot, T. Frederiksen, M. Brandbyge, and R. Berndt
Controlled contact to a C60 molecule
Phys. Rev. Lett. 98, 065502 (2007) [PRL Cover] [ PDF ] [cond-mat/0608476].

The tip of a low-temperature scanning tunneling microscope is approached towards a C60 molecule adsorbed at a pentagon-hexagon bond on Cu(100) to form a tip-molecule contact. The conductance rapidly increases to ~0.25 conductance quanta in the transition region from tunneling to contact. Ab-initio calculations within density functional theory and nonequilibrium Green's function techniques explain the experimental data in terms of the conductance of an essentially undeformed C60. The conductance in the transition region is affected by structural fluctuations which modulate the tip-molecule distance.

T. Frederiksen
Inelastic transport theory for nanoscale systems
PhD thesis, MIC, DTU, February 2007. [ PDF ]

This thesis describes theoretical and numerical investigations of inelastic scattering and energy dissipation in electron transport through nanoscale systems. A computational scheme, based on a combination of density functional theory (DFT) and nonequilibrium Green's functions (NEGF), has been developed to describe the electrical conduction properties taking into account the full atomistic details of the systems. The scheme involves quantitative calculations of electronic structure, vibrational modes and frequencies, electron-vibration couplings, and inelastic current-voltage characteristics in the weak coupling limit.

When a current is passed through a nanoscale device, such as a single molecule or an atomic-size contact, it will heat up due to excitations of the nuclear vibrations. The developed scheme is able to quantify this local heating effect and to predict how it affects the conductance.

The methods have been applied to a number of specific systems, including monatomic gold chains, atomic point contacts, and metal-molecule-metal configurations. These studies have clarified the inelastic effects in the electron transport and characterized the vibrational modes that couple to the current. For instance, the dominant scattering for gold chains could be traced back to the longitudinal "alternating bond-length" mode. Furthermore, the results have been compared critically with experimental measurements for the different systems, and provided a microscopic understanding for the important physics. An example is the current-induced fluctuations that have been shown to influence the transport though individual C 60 molecules on copper surfaces.

M. Paulsson, T. Frederiksen, and M. Brandbyge
Inelastic transport through molecules: comparing first-principles calculations to experiments
Nano Lett. 6, 258-262 (2006) [ PDF ]

We present calculations of the elastic and inelastic conductance through three different hydrocarbon molecules connected to gold electrodes. Our method is based on a combination of the nonequilibrium Green's function method with density functional theory. Vibrational effects in these molecular junctions were previously investigated experimentally by Kushmerick et al. (Nano Lett. 2004, 4, 639). Our results are in good agreement with the measurements and provide insights into (i) which vibrational modes are responsible for inelastic scattering, (ii) the width of the inelastic electron tunneling signals, and (iii) the mechanisms of heating and cooling of the vibrational modes induced by the coupling to the charge carriers.

M. Paulsson, T. Frederiksen, and M. Brandbyge
Phonon scattering in nanoscale systems: lowest order expansion of the current and power expressions
J. Phys.: Conf. Ser. 35, 247-254 (2006) [ PDF ]

We use the non-equilibrium Green's function method to describe the effects of phonon scattering on the conductance of nano-scale devices. Useful and accurate approximations are developed that both provide (i) computationally simple formulas for large systems and (ii) simple analytical models. In addition, the simple models can be used to fit experimental data and provide physical parameters.

M. Paulsson, T. Frederiksen, and M. Brandbyge
Modeling inelastic phonon scattering in atomic- and molecular-wire junctions
Phys. Rev. B 72, 201101(R) (2005); 75, 129901(E) (2007) [ PDF ] [cond-mat/0505473]

Computationally inexpensive approximations describing electron-phonon scattering in molecular-scale conductors are derived from the nonequilibrium Green's function method. The accuracy is demonstrated with a first-principles calculation on an atomic gold wire. Quantitative agreement between the full nonequilibrium Green's function calculation and the newly derived expressions is obtained while simplifying the computational burden by several orders of magnitude. In addition, analytical models provide intuitive understanding of the conductance including nonequilibrium heating and provide a convenient way of parameterizing the physics. This is exemplified by fitting the expressions to the experimentally observed conductances through both an atomic gold wire and a hydrogen molecule.

M. C. Sullivan, D. R. Strachan, T. Frederiksen, R. A. Ott, and C. J. Lobb
Effects of self-field and low magnetic fields on the normal-superconducting phase transition
Phys. Rev. B 72, 092507 (2005) [ PDF ] [cond-mat/0505334].

Researchers have studied the normal-superconducting phase transition in the high-Tc cuprates in a magnetic field (the vortex-glass or Bose-glass transition) and in zero field. Often, transport measurements in "zero field" are taken in the Earth's ambient field or in the remnant field of a magnet. We show that fields as small as the Earth's field will alter the shape of the current vs voltage curves and will result in inaccurate values for the critical temperature Tc and the critical exponents ν and z, and can even destroy the phase transition. This indicates that without proper screening of the magnetic field it is impossible to determine the true zero-field critical parameters, making correct scaling and other data analysis impossible. We also show, theoretically and experimentally, that the self field generated by the current flowing in the sample has no effect on the current vs voltage isotherms.

T. Frederiksen, M. Brandbyge, N. Lorente, and A. P. Jauho
Modeling of inelastic transport in one-dimensional metallic atomic wires
J. Comp. Electronics 3, 423-427 (2004) [ PDF ] [cond-mat/0411108]

Inelastic effects in electron transport through nano-sized devices are addressed with a method based on nonequilibrium Green's functions (NEGF) and perturbation theory to infinite order in the electron-vibration coupling. We discuss the numerical implementation which involves an iterative scheme to solve a set of coupled non-linear equations for the electronic Green's functions and the self-energies due to vibrations. To illustrate our method, we apply it to a one-dimensional single-orbital tight-binding description of the conducting electrons in atomic gold wires, and show that this simple model is able to capture most of the essential physics.

T. Frederiksen, M. Brandbyge, N. Lorente, and A. P. Jauho
Inelastic scattering and local heating in atomic gold wires
Phys. Rev. Lett. 93, 256601 (2004) [ PDF ] [cond-mat/0410700]

We present a method for including inelastic scattering in a first-principles density-functional computational scheme for molecular electronics. As an application, we study two geometries of four-atom gold wires corresponding to two different values of strain and present results for nonlinear differential conductance vs device bias. Our theory is in quantitative agreement with experimental results and explains the experimentally observed mode selectivity. We also identify the signatures of phonon heating.

M. C. Sullivan, T. Frederiksen, J. M. Repaci, D. R. Strachan, R. A. Ott, and C. J. Lobb
Normal-superconducting phase transition mimicked by current noise
Phys. Rev. B 70, 140503(R) (2004) [ PDF ] [cond-mat/0407144]

As a superconductor goes from the normal state into the superconducting state, the voltage versus current characteristics at low currents change from linear to nonlinear. We show theoretically and experimentally that the addition of current noise to nonlinear voltage versus current curves will create ohmic behavior. Ohmic response at low currents for temperatures below the critical temperature Tc mimics the phase transition and leads to incorrect values for Tc and the critical exponents ν and z. The ohmic response occurs at low currents, and will occur in both the zero-field transition and the vortex-glass transition. Our results indicate that the transition temperature and critical exponents extracted from the conventional scaling analysis are inaccurate if current noise is not filtered out. This is a possible explanation for the wide range of critical exponents found in the literature.

D. R. Strachan, M. C. Sullivan, T. Frederiksen, R. A. Ott, and C. J. Lobb
What a superconducting transition should look like: extrapolating data from scaling plots
Physica C 408-410, 562-563 (2004) [ PDF ]

We compare measured current-voltage measurements of a YBa2Cu3O7-δ film with data extrapolated from various scaling collapses. We find that in general the extrapolated data show opposite concavity about the transition temperature at all currents; whereas the experimental data do not. This indicates that the experiments do not demonstrate unambiguous evidence for a superconducting transition.

M. C. Sullivan, D. R. Strachan, T. Frederiksen, R. A. Ott, M. Lilly, and C. J. Lobb
Zero-field superconducting phase transition obscured by finite-size effects in thick YBa2Cu3O7-δ films
Phys. Rev. B 69, 214524 (2004) [ PDF ] [cond-mat/0308258]

We report on the normal-superconducting phase transition in thick YBa2Cu3O7-δ films in zero magnetic field. We find significant finite-size effects at low currents even in our thickest films (d=3200 Å). Using data at higher currents, we can unambiguously find Tc and z, and show z=2.1±0.15, as expected for the three-dimensional XY model with diffusive dynamics. The crossover to two-dimensional behavior, seen by other researchers in thinner films (d ≤ 500 Å), obscures the three-dimensional transition in both zero field and the vortex-glass transition in field, leading to incorrect values of Tc (or Tg), ν, and z. The finite-size effects, usually ignored in thick films, are an explanation for the wide range of critical exponents found in the literature.

T. Frederiksen
Inelastic electron transport in nanosystems
MSc thesis, MIC, DTU, February 2004. [ PDF ]

The emerging field of molecular electronics, in which individual molecules play the role of active devices, is receiving much attention due to its possible technological impact. Recent advances in nanoscale fabrication and engineering techniques have made it possible to study the transport properties of devices on the atomic scale. At this level one inherently probes the quantum mechanical nature of matter which manifests a number of effects not well understood yet. One such effect is the mutual interaction between electrical current and atomic vibrations.

In this thesis we describe a method for calculating dc current-voltage characteristics of nanostructures connected between metallic leads taking into account electron-vibration scattering inside the device. The method is based on nonequilibrium Green's functions (NEGF) and a Meir-Wingreen type formula for the current through an interacting region of space. Within the Born-Oppenheimer approximation we calculate the electronic Green's functions for this region treating the electron-phonon interaction perturbatively in the self-consistent Born approximation. The numerical implementation of the present method is discussed in detail, and we compare it with results in the literature as well as with our own calculations based on an exact diagonalization technique.

In particular we look at transport through metallic wires of single atoms. With a simple single-orbital tight-binding model and parameters fitted for Au chains we show how to determine the normal modes of vibration, the electron-vibration couplings, and the influence of the different modes on the conductance. Finally, we discuss the potential of combining our method with ab initio calculations of electronic structure, vibrational modes, and couplings, and present some preliminary results in this direction.