Analytical solution to the surface states of antiferromagnetic topological insulator MnBi$_2$Te$_4$

Hai-Peng Sun, C. M. Wang, Song-Bo Zhang, Rui Chen, Hai-Zhou Lu, X. C. Xie

Published 2020-09-23Version 1

Recently, the intrinsic magnetic topological insulator MnBi$_2$Te$_4$ has attracted great attention. It has an out-of-plane antiferromagnetic order, which is believed to open a sizable energy gap in the surface states. This gap, however, was not always observable in the latest ARPES experiments. To address this issue, we analytically derive an effective model for the 2D surface states by starting from a 3D Hamiltonian for bulk MnBi$_2$Te$_4$ and taking into account the spatial profile of the bulk magnetization. We suggest that the Bi antisite defects in the Mn atomic layers in the bulk may be one of the reasons for the varied experimental results, since the Bi antisite defects may result in a much smaller and more localized intralayer ferromagnetic order, leading to the diminished surface gap. In addition, we calculate the spatial distribution and penetration depth of the surface states, which are mainly embedded in the first two septuple layers from the terminating surface. From our analytical results, the influence of the bulk parameters on the surface states can be found explicitly. Furthermore, we derive a $\bf{k}\cdot \bf{p}$ model for MnBi$_2$Te$_4$ thin films and show the oscillation of the Chern number between odd and even septuple layers. Our results will be helpful for the ongoing explorations of the MnBi$_x$Te$_y$ family.