Simple model for the gap in the surface states of the antiferromagnetic topological insulator MnBi$_2$Te$_4$

TL;DR

This paper presents a simple effective model for understanding the surface state gaps in antiferromagnetic topological insulator MnBi$_2$Te$_4$, highlighting how magnetic order and surface perturbations influence the electronic spectrum.

Contribution

It introduces a minimal Hamiltonian capturing the impact of antiferromagnetic order and surface potential shifts on the surface states of MnBi$_2$Te$_4$.

Findings

Gapless surface states are protected by symmetries in pristine conditions.

Surface potential shifts can open a gap in the surface spectrum.

Disorder does not alter the topological nature of the system.

Abstract

We study the influence of the antiferromagnetic order on the surface states of topological insulators. We derive an effective Hamiltonian for these states, taking into account the spatial structure of the antiferromagnetic order. We obtain a typical (gapless) Dirac Hamiltonian for the surface states when the surface of the sample is not perturbed. Gapless spectrum is protected by the combination of time-reversal and half-translation symmetries. However, a shift in the chemical potential of the surface layer opens a gap in the spectrum away from the Fermi energy. Such a gap occurs only in systems with finite antiferromagnetic order. We observe that the system topology remains unchanged even for large values of the disorder. We calculate the spectrum using the tight-binding model with different boundary conditions. In this case we get a gap in the spectrum of the surface states. This discrepancy arises due to the violation of the combined time-reversal symmetry. We compare our results with experiments and density functional theory calculations.