Moir\'e surface states and "high-temperature" superconductivity in topological insulators
Recently, moire superlattices have been found on the surface of topological insulators (TI) due to the rotational misalignment of topmost layers. In this work, we study the effects of moire superlattices on the topological surface states. We introduce a continuum model of Dirac electrons moving in the periodic potential to describe the moire surface states and identify various (high-order) van Hove singularities (VHS), which explains the experimentally observed peaks in the density of states (DOS). We show that the power-law divergent DOS at high-order VHS significantly enhances electron-phonon superconductivity. By solving the gap equation, we derive an analytic formula for the transition temperature $T_c$, which exhibits a power-law dependence on the retarded electron-phonon interaction strength $\lambda^*$.