Koopmans' theorem as the mechanism of nearly gapless surface states in self-doped magnetic topological insulators

Abstract

The magnetization-induced gap at the surface state is widely believed as the kernel of magnetic topological insulators (MTIs) because of its relevance to various topological phenomena, such as the quantum anomalous Hall effect and the axion insulator phase. However, if the magnetic gap exists in an intrinsic MTI, such as MnBi$_{2}$Te$_{4}$, still remains elusive, with significant discrepancies between theoretical predictions and various experimental observations. Here, including the previously overlooked self-doping in real MTIs, we find that in general a doped MTI prefers a ground state with a gapless surface state. We use a simple model based on Koopmans' theorem to elucidate the mechanism and further demonstrated it in self-doped MnBi$_{2}$Te$_{4}$/(Bi$_{2}$Te$_{3}$)$_{n}$ family through first-principles calculations. Our work shed light on the design principles of MTIs with magnetic gaps by revealing the critical role of doping effects in understanding the delicate interplay between magnetism and topology.