Graphene nanostructures, where quantum confinement opens an energy gap in the band structure, hold promise for future electronic devices. To realize the full potential of these materials, atomic-scale control over the contacts to graphene and the graphene nanostructure forming the active part of the device is required. The contacts should have a high transmission and yet not modify the electronic properties of the active region significantly to maintain the potentially exciting physics offered by the nanoscale honeycomb lattice. Here we show how contacting an atomically well-defined graphene nanoribbon to a metallic lead by a chemical bond via only one atom significantly influences the charge transport through the graphene nanoribbon but does not affect its electronic structure. Specifically, we find that creating well-defined contacts can suppress inelastic transport channels.

All material supplied via Aaltodoc is protected by copyright and other intellectual property rights, and duplication or sale of all or part of any of the repository collections is not permitted, except that material may be duplicated by you for your research use or educational purposes in electronic or print form. You must obtain permission for any other use. Electronic or print copies may not be offered, whether for sale or otherwise to anyone who is not an authorised user. An extended tight-binding model that includes up to third-nearest-neighbor hopping and a Hubbard meanfield interaction term is tested against ab initio local spin-density approximation results of band structures for armchair-and zigzag-edged graphene nanoribbons. A single tight-binding parameter set is found to accurately reproduce the ab initio results for both the armchair and zigzag cases. Transport calculations based on the extended tight-binding model faithfully reproduce the results of ab initio transport calculations of graphene nanoribbon-based systems.

The electronic properties of graphene edges have been predicted to depend on their crystallographic orientation. The so-called zigzag (ZZ) edges haven been extensively explored theoretically and proposed for various electronic applications. However, their experimental study remains challenging due to the difficulty in realizing clean ZZ edges without disorder, reconstructions, or the presence of chemical functional groups. Here, we propose the ZZ-terminated, atomically sharp interfaces between graphene and hexagonal boron nitride (BN) as experimentally realizable, chemically stable model systems for graphene ZZ edges. Combining scanning tunneling microscopy and numerical methods, we explore the structure of graphene-BN interfaces and show them to host localized electronic states similar to those on the pristine graphene ZZ edge.

Despite the enormous interest in the properties of graphene and the potential of graphene nanostructures in electronic applications, the study of quantum-confined states in atomically well-defined graphene nanostructures remains an experimental challenge. Here, we study graphene quantum dots (GQDs) with well-defined edges in the zigzag direction, grown by chemical vapor deposition on an Ir(111) substrate by low-temperature scanning tunneling microscopy and spectroscopy. We measure the atomic structure and local density of states of individual GQDs as a function of their size and shape in the range from a couple of nanometers up to ca. 20 nm. The results can be quantitatively modeled by a relativistic wave equation and atomistic tight-binding calculations. The observed states are analogous to the solutions of the textbook "particle-in-a-box" problem applied to relativistic massless fermions.

Phase coherence of charge carriers leads to electron-wave interference in ballistic mesoscopic conductors [1]. In graphene, such Fabry-Pérot-like interference has been observed [2-5], but a detailed analysis has been complicated by the two-dimensional nature of conduction, which allows for complex interference patterns [6][7][8]. In this work, we have achieved high-quality Fabry-Pérot interference in a suspended graphene device, both in conductance and in shot noise, and analyzed their structure using Fourier transform techniques. The Fourier analysis reveals two sets of overlapping, coexisting interferences, with the ratios of the diamonds being equal to the width to length ratio of the device. We attribute these sets to a unique coexistence of longitudinal and transverse resonances, with the longitudinal resonances originating from the bunching of modes with low transverse momentum. Furthermore, our results give insight into the renormalization of the Fermi velocity in suspended graphene samples, caused by unscreened many-body interactions [9].

We implement, optimize, and validate the linear-scaling Kubo-Greenwood quantum transport simulation on graphics processing units by examining resonant scattering in graphene. We consider two practical representations of the Kubo-Greenwood formula: a Green-Kubo formula based on the velocity auto-correlation and an Einstein formula based on the mean square displacement. The code is fully implemented on graphics processing units with a speedup factor of up to 16 (using double-precision) relative to our CPU implementation. We compare the kernel polynomial method and the Fourier transform method for the approximation of the Dirac delta function and conclude that the former is more efficient. In the ballistic regime, the Einstein formula can produce the correct quantized conductance of one-dimensional graphene nanoribbons except for an overshoot near the band edges. In the diffusive regime, the Green-Kubo and the Einstein formalisms are demonstrated to be equivalent. A comparison of the lengthdependence of the conductance in the localization regime obtained by the Einstein formula with that obtained by the non-equilibrium Green's function method reveals the challenges in defining the length in the Kubo-Greenwood formalism at the strongly localized regime.

Ijäs, M.; Ervasti, M.; Uppstu, Christer; Liljeroth, Peter; van der Lit, J.; Swart, I.; Harju, A. We study the electronic structure of finite armchair graphene nanoribbons using density-functional theory and the Hubbard model, concentrating on the states localized at the zigzag termini. We show that the energy gaps between end-localized states are sensitive to doping, and that in doped systems, the gap between the end-localized states decreases exponentially as a function of the ribbon length. Doping also quenches the antiferromagnetic coupling between the end-localized states leading to a spin-split gap in neutral ribbons. By comparing dI/dV maps calculated using the many-body Hubbard model, its mean-field approximation and density-functional theory, we show that the use of a single-particle description is justified for graphene π states in case spin properties are not the main interest. Furthermore, we study the effect of structural defects in the ribbons on their electronic structure. Defects at one ribbon terminus do not significantly modify the electronic states localized at the intact end. This provides further evidence for the interpretation of a multipeak structure in a recent scanning tunneling spectroscopy (STS) experiment resulting from inelastic tunneling processes [van der Lit et al., Nat. Commun. 4, 2023]. Finally, we show that the hydrogen termination at the flake edges leaves identifiable fingerprints on the positive bias side of STS measurements, thus possibly aiding the experimental identification of graphene structures. Electronic states in finite graphene nanoribbons: Effect of charging and defects

We study Anderson localization in graphene with short-range disorder using the real-space Kubo-Greenwood method implemented on graphics processing units. Two models of short-range disorder, namely, the Anderson on-site disorder model and the vacancy defect model, are considered. For graphene with Anderson disorder, localization lengths of quasi-one-dimensional systems with various disorder strengths, edge symmetries, and boundary conditions are calculated using the real-space Kubo-Greenwood formalism, showing excellent agreement with independent transfer matrix calculations and superior computational efficiency. Using these data, we demonstrate the applicability of the one-parameter scaling theory of localization length and propose an analytical expression for the scaling function, which provides a reliable method of computing the two-dimensional localization length. This method is found to be consistent with another widely used method which relates the two-dimensional localization length to the elastic mean free path and the semiclassical conductivity. Abnormal behavior at the charge neutrality point is identified and interpreted to be caused by finite-size effects when the system width is comparable to or smaller than the elastic mean free path. We also demonstrate the finite-size effect when calculating the two-dimensional conductivity in the localized regime and show that a renormalization group beta function consistent with the one-parameter scaling theory can be extracted numerically. For graphene with vacancy disorder, we show that the proposed scaling function of localization length also applies. Lastly, we discuss some ambiguities in calculating the semiclassical conductivity around the charge neutrality point due to the presence of resonant states.