Nanoelectronics – theory and simulation


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
submitted [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.

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.

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., accepted (2023)

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) [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) [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.