Propagating edge and interfacial states in corrugated graphene: Robustness and configurability
Periodically strained graphene on patterned substrates provides a versatile route to realizing moiré-like electronic structures through strain engineering. Here, we show that the interplay between a strain-induced pseudomagnetic field and a displacement-field-controlled scalar potential enables the formation of isolated narrow bands and multiple energy gaps near charge neutrality and at higher energies. Some of the low-energy bands exhibit nontrivial topology, carrying valley-opposite Chern numbers. Remarkably, despite a vanishing total Chern number, propagating in-gap edge states emerge in a wide range of nanoribbon geometries that preserve valley symmetry. We elucidate the distinct mechanisms responsible for edge states in the zero-energy and higher-energy gaps and demonstrate that they remain robust against variations in superlattice termination and moderate disorder, despite lacking conventional topological protection. Leveraging these properties, we propose device architectures in which an externally applied staggered potential electrically switches the zero-energy gap and its associated edge channels on and off. Furthermore, split-gate geometries generate topologically protected interfacial states that coexist with the edge modes and can be spatially reconfigured by gate voltages. These results establish strain superlattices as a powerful platform for engineering topological electronic states and electronic transport in graphene.