Analytical solution for the surface states of antiferromagnetic topological insulator MnBi${}_2$Te${}_4$

Abstract

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 angle-resolved photoemission spectroscopy (ARPES) experiments. To address this issue, we analytically derive an effective model for the two-dimensional (2D) surface states by starting from a three-dimensional (3D) Hamiltonian for bulk MnBi${}_2$Te${}_4$ and taking into account the spatial profile of the bulk magnetization. Our calculations suggest that the diminished surface gap may be caused by a much smaller and more localized intralayer ferromagnetic order. In addition, we calculate the spatial distribution and penetration depth of the surface states, which indicates that the surface states 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 $\mathbf{k}\cdot \mathbf{p}$ 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.

arXiv comment6 pages, 3 figures

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• Dissipative Edge Transport in Disordered Axion Insulator Films
• Electrostatic effects of the MnBi2Te4-superconductor hetero-structures in chiral Majorana search
• Electrically tunable high-Chern-number quasiflat bands in twisted antiferromagnetic topological insulators
• Emergent Weyl-like points in periodically modulated systems
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• Conductance oscillations of antiferromagnetic layer tunnel junctions
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