Charge and spin transport anisotropy in nanopatterned graphene

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.