Facet dependent surface energy gap on magnetic topological insulators

Magnetic topological insulators (MnBi₂Te₄)(Bi₂Te₃)_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 Bi₂Te₃ layer introduces versatility to engineer electronic and magnetic properties. However, whether surface states on the Bi₂Te₃ 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 Bi₂Te₃ terminated facets are gapless for n≥1 compounds by calculations. Although the surface Bi₂Te₃ (one layer or more) and underlying MnBi₂Te₄ layers hybridize and give rise to a gap, such a hybridization gap may overlap 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 Bi₂Te₃ surface. In theory, the insulating phase can still be realized in a film if both surfaces are MnBi₂Te₄ layers. Otherwise, it requires that the film thickness be less than 10-20nm 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.