Higher-Order Van Hove Singularities on Moir'e Surface States of Topological Insulators

Three-dimensional topological insulators (TIs) are bulk insulators with exotic metallic surface states that host symmetry-protected 2D Dirac fermions. Recent experiments have demonstrated the formation of Moir'e superlattices that renormalize the velocity of the low energy Dirac excitations on the 3D TI surface, thus promoting the formation of exotic many-body states. Here, we investigate the effects of Moir'e superlattices on the topological surface states using a continuum model of Dirac fermions in a periodic potential and Zeeman field. We find a low-energy Chern band supporting tunable higher-order Van Hove singularities (HOVHS) for a manifold of superlattice potential and Zeeman field strengths which obey a scaling relation. An effective tight-binding model is also studied to gain a better understanding of the formation of the HOVHS in the Moir'e bandstructure. This framework opens a new path to explore interaction effects on the surface of TI.