Three-Dirac-fermion approach to unexpected universal gapless surface states of van der Waals magnetic topological insulators

Layered van der Waals (vdW) topological materials, especially the recently discovered MnBi$_2$Te$_4$-family magnetic topological insulators (TIs), have aroused great attention. However, there has been a serious debate about whether the surface states are gapped or gapless for antiferromagnetic (AFM) TI MnBi$_2$Te$_4$, which is crucial to the prospect of various magnetic topological phenomena. Here, a minimal three-Dirac-fermion approach is developed to generally describe topological surface states of nonmagnetic/magnetic vdW TIs under the modulation of the interlayer vdW gap. In particular, this approach is applied to address the controversial issues concerning the surface states of vdW AFM TIs. Remarkably, topologically protected gapless Dirac-cone surface states are found to arise due to a small expansion of the interlayer vdW gap on the surface, when the Chern number equals zero for the surface ferromagnetic layer; while the surface states remain gapped in all other cases. These results are further confirmed by our first-principles calculations on AFM TI MnBi$_2$Te$_4$. The theorectically discovered gapless Dirac-cone states provide a unique mechanism for understanding the puzzle of the experimentally observed gapless surface states in MnBi$_2$Te$_4$. This work also provides a promising way for experiments to realize the intrinsic magnetic quantum anomalous Hall effect in MnBi$_2$Te$_4$ films with a large energy gap.