Magnetic topological insulators (MnBi 2 Te 4 )(Bi 2 Te 3 ) n (n = 0, 1, 2, 3) are promising to realize exotic topological states such as the quantum anomalous Hall effect (QAHE) and axion insulator (AI), where the Bi 2 Te 3 layer introduces versatility to engineer electronic and magnetic properties.However, whether surface states on the Bi 2 Te 3 terminated facet are gapless or gapped is debated, and its consequences in thin-film properties are rarely discussed. In this work, we find that the Bi 2 Te 3 terminated facets are gapless for n ≥ 1 compounds by calculations. Despite that the surface Bi 2 Te 3 (one layer or more) and underlying MnBi 2 Te 4 layers hybridize and give rise to a gap, such a hybridization gap overlaps with bulk valence bands, leading to a gapless surface after all. Such a metallic surface poses a fundamental challenge to realize QAHE or AI, which requires an insulating gap in thin films with at least one Bi 2 Te 3 surface. In theory, the insulating phase can still be realized in a film if both surfaces are MnBi 2 Te 4 layers. Otherwise, it requires that the film thickness is less than 10∼20 nm to push down bulk valence bands via the size effect. Our work paves the way to understand surface states and design bulk-insulating quantum devices in magnetic topological materials.