Charge and spin transport anisotropy in nanopatterned graphene

Abstract

Anisotropic electronic transport is a possible route towards nanoscale circuitry design, particularly in two-dimensional materials. Proposals to introduce such a feature in patterned graphene have to date relied on large-scale structural inhomogeneities. Here we theoretically explore how a random, yet homogeneous, distribution of zigzag-edged triangular perforations can generate spatial anisotropies in both charge and spin transport. Anisotropic electronic transport is found to persist under considerable disordering of the perforation edges, suggesting its viability under realistic experimental conditions. Furthermore, controlling the relative orientation of perforations enables spin filtering of the transmitted electrons, resulting in a half-metallic anisotropic transport regime. Our findings point towards a co-integration of charge and spin control in a two-dimensional platform of relevance for nanocircuit design. We further highlight how geometrical effects allow finite samples to display finite transverse resistances, reminiscent of Spin Hall effects, in the absence of any bulk fingerprints of such mechanisms, and explore the underlying symmetries behind this behaviour. approach based on uniformly distributed perforations, where the anisotropic behavior is dictated by the atomiclevel properties of the perforation edges.Extended edges with the zigzag (zz) geometry locally break sublattice symmetry, leading to the formation of localized states [21,22], and to the formation of local magnetic moments when electron-electron interactions are considered [23][24][25][26][27]. Local moments of opposite sign occur at the edges associated with different sublattices, so that global ferromagnetism can only occur when the overall sublattice symmetry is broken [23,28,29], in accordance with Lieb's theorem [30]. This does not occur for zz-edged nanoribbons [31] or perforations containing edges equally divided between the sublattices [32]. However, the three edges of a zz-edged triangular graphene antidot (zz-TGA) are all associated with a single sublattice, which dictates large ferromagnetic moments [8, 33-37] (see figure 1).Recent works have demonstrated that lattices of approximately 1 nm side length zz-TGAs provide an excellent platform for electronic and spintronic applications due to robust band gaps, half-metallicity, and spinsplitting properties [8,9]. In the case of spin-splitting, incoming currents can be directed into output leads according to their spin orientation. Such behavior is analogous to the spin Hall effect [38], but without relying on spin-orbit coupling (SOC) effects. These features were shown to be robust against disorder, unlike those in other antidot geometries, due to their dependence on local symmetry breaking effects and cumulative scattering from multiple antidots, and not on the exact separation and size of perforations. With state-of-the-art lithographic methods, triangular holes in graphene [39], as well as zz-etched nanostructures [40][41][42], can be realised. Alternatively, a patterned laye...

Predicting magnetic edge behaviour in graphene using neural networks

“…For example, triangular flakes can have a sublattice imbalance, resulting in a net magnetisation [7]. Similar behaviour is predicted for subtractive antidot systems [24][25][26], where ZZ-edged perforations underpin half-metallic [27] and anisotropic transport [28].…”

Tunable valley Hall effect in gate-defined graphene superlattices

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Linear scaling quantum transport methodologies

“…Others studies combining O(N ) bulk Kubo approaches with multiterminal Landauer-Büttiker quantum transport methods have revealed more complexity in understanding the physics of the SHE than can be obtained from a simple theoretical interpretation of experimental data. For instance, Gregersen and coworkers have demonstrated how geometrical effects allow finite samples to display transverse resistances that are reminiscent of the SHE, but which disappear in the bulk limit (Gregersen et al, 2018). Another important finding concerns the parasitic background contributions that appear when calculating the nonlocal resistance of chemically functionalized graphene systems, which can mask spin effects or mislead the interpretation of experiments (Van Tuan et al, 2016a).…”