Topological surface states of Mn Bi 2 Te 4 at finite temperatures and at domain walls

$\mathrm{Mn}{\mathrm{Bi}}_{2}{\mathrm{Te}}_{4}$ 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 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 N\'eel temperature. In addition, we examine the effect of magnetic domains on the electronic structure, and we find that the domain wall zero-gap states extend over many unit-cells. These domain wall states can appear similar to the high-temperature topological surface state when many domain sizes are averaged, potentially reconciling theoretical results with experiments.