Features of surface states of an intrinsic antiferromagnetic topological insulator with a noncollinear texture of domain walls

The formation of a magnetic order in a three-dimensional topological insulator is manifested in the behavior of electronic states at its boundaries. The modification of the surface electronic structure under the effect of a noncollinear domain-wall magnetization texture appearing in an intrinsic antiferromagnetic topological insulator is theoretically studied in this work. It is shown that a bound one-dimensional state induced by a domain wall appears in addition to the modulation of the surface exchange gap and the shift of the two-dimensional Dirac cone in the momentum space. The main characteristics of the bound state such as the energy spectrum, spin polarization, spatial localization, and their dependence on the mutual orientation of magnetizations in domains are described. Methods of the experimental detection of a one-dimensional state associated with a domain wall, as well as a possible contribution of this state to new quantum effects, on the surface of the antiferromagnetic topological insulator such as MnBi$_2$Te$_4$ are discussed.