Antidot superlattices in two-dimensional topological insulators

Abstract

We investigate the electronic properties of a two-dimensional topological insulator patterned with an array of circular holes. The band structures of the topological insulator superlattices are calculated using the Bernevig-Hughes-Zhang model, discretized with the finite element method. The band topology is studied using the Fukui-Hatsugai-Suzuki method, exploiting the fact that topological charge is conserved when a band gap closes and reopens. We find that when the holes are close to each other and the edge states overlap significantly, the material loses its topological character and becomes a trivial insulator. The results show that patterning topological insulators changes their properties, and this can be achieved with a feature size compatible with current lithographic techniques. This shows the potential to incorporate patterned topological insulators in future electronics.