Topological surfaces states of MnBi₂Te₄ at finite temperatures and at domain walls

MnBi₂Te₄ has recently been the subject of intensive study, due
to the prediction of axion insulator, Weyl semimetal, and quantum
anomalous Hall insulator phases, depending on the structure and
magnetic ordering. Experimental results have confirmed some aspects of
this picture, but several experiments have seen zero-gap topological
surfaces states at low temperature, in conflict with expectations. In
this work, we develop a first-principles-based tight-binding model
that allows for arbitrary control of the local spin direction and
spin-orbit coupling, enabling us to accurately treat large
unit-cells. Using this model, we examine the behavior of the
topological surface state as a function of temperature, finding a gap
closure only above the Neel temperature. In addition, we examine the effect of
magnetic domains on the electronic structure, finding that the domain
wall zero-gap states extend over many unit-cells and can mimic the
high temperature topological surface state when many domains
are averaged over, potentially reconciling theoretical results with
experiments.