  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.
