We report on the emergence of bulk, valley-polarized currents in graphene-based devices, driven by spatially varying regions of broken sublattice symmetry, and revealed by nonlocal resistance (R NL ) fingerprints. By using a combination of quantum transport formalisms, giving access to bulk properties as well as multiterminal device responses, the presence of a nonuniform local band gap is shown to give rise to valley-dependent scattering and a finite Fermi-surface contribution to the valley Hall conductivity, related to characteristics of R NL . These features are robust against disorder and provide a plausible interpretation of controversial experiments in graphene/hexagonal boron nitride superlattices. Our findings suggest both an alternative mechanism for the generation of valley Hall effect in graphene and a route towards valley-dependent electron optics, by materials and device engineering.

Recent experimental findings and theoretical predictions suggest that nitrogen-doped CVD-grown graphene may give rise to electronic band gaps due to impurity distributions which favour segregation on a single sublattice. Here we demonstrate theoretically that such distributions lead to more complex behaviour in the presence of edges, where geometry determines whether electrons in the sample view the impurities as a gap-opening average potential or as scatterers. Zigzag edges give rise to the latter case, and remove the electronic bandgaps predicted in extended graphene samples. We predict that such behaviour will give rise to leakage near grain boundaries with a similar geometry or in zigzag-edged etched devices. Furthermore, we examine the formation of one-dimensional metallic channels at interfaces between different sublattice domains, which should be observable experimentally and offer intriguing waveguiding possibilities.