  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.
