Magic-Angle Physics in Two-Dimensional Topological Insulators

The Bernevig-Hughes-Zhang (BHZ) model is a quintessential model for a two-dimensional Z₂ topological insulator with topological and trivial insulator phases separated from each other by semimetallic critical points. We study the fate of the BHZ model in the presence of a quasiperiodic potential by using the kernel polynomial method to calculate the density of states and conductivity to determine the zero temperature phase diagram. The semimetal undergoes magic-angle transitions driven by the quasiperiodic potential, which generates flat bands at the transition to a metallic phase similar to other two-dimensional systems with Dirac nodes. Additionally, the topological insulating phases undergo quantum phase transitions into a metallic phase due to the quasiperiodic potential closing the insulating band gap. Lastly, we also study how the surface states strongly renormalize due to these unique quasiperiodic driven transitions.