Magic angles for topological surface states in twisted heterostructures

Twisted bilayer graphene has been a center of recent theoretical and experimental interest due to the emergence of magic angles and the resulting tunable interaction-driven phases induced in the flat bands. Motivated by these results, we study a related class of systems: twisted interfaces between Dirac materials in which one layer is the surface state of a topological insulator (TI). Using both perturbation theory and global calculations of the band structure, we study two specific scenarios: the interface between two 3D TIs and the interface between graphene and a 3D TI. We derive the conditions to realize a magic angle where the velocity of the TI surface state vanishes. However, in the simplest models, flat bands only result if the interlayer hopping includes spin-flipping terms. We discuss the possibility of realizing magic angles in spite of this constraint.

Reference:  https://arxiv.org/abs/2112.11464