Topological Bloch Bands in Graphene Superlattices

We outline an approach to endow a plain vanilla material with topological properties by creating topological bands in stacks of manifestly nontopological atomically thin materials. The approach is illustrated with a model system comprised of graphene stacked atop hexagonal-boron-nitride. In this case, the Berry curvature of the electron Bloch bands is highly sensitive to the stacking configuration. As a result, electron topology can be controlled by crystal axes alignment, granting a practical route to designer topological materials. Berry curvature manifests itself in transport via the valley Hall effect and long-range chargeless valley currents. The non-local electrical response mediated by such currents provides diagnostics for band topology.