Modeling of Meta-Graphene and Valleytronics on a Semiconductor

Two-dimensional materials fabricated as periodic nanostructures on a semiconducting surface offer versatile tunability. Adjusting the parameters of the nanopatterning alters the electronic properties of the material, thus opening new possibilities for designing novel electronic devices and exploring quantum geometric phenomena. In this work we model the electronic properties of artificially-tailored semiconducting quantum materials (such as meta-graphene and related valley Hall topological insulators), including the topological properties of interface states. To this end we consider a two-dimensional electron gas system patterned with periodic potentials. Using parameters achievable experimentally, we demonstrate systems exhibiting nonzero valley Chern numbers that protect the existence of domain wall edge states. We perturb these domain wall edge states with both charge-puddle induced disorder and random imperfections in the periodic potential and confirm they are robust under realistic experimental conditions.