Electronic spectrum features under the transition from axion insulator phase to quantum anomalous hall effect phase in an intrinsic antiferromagnetic topological insulator thin film

In this paper, we investigate the electron topological states in a thin film of intrinsic antiferromagnetic topological insulator, focusing on their relationship with the magnetic texture. We consider a model for the film with an even number of septuple-layer blocks, which is subject to transition from the phase of an axion insulator to the phase of quantized Hall conductivity under an external magnetic field. In the continuum approach, we model an effective two-dimensional Hamiltonian of the thin film of a topological insulator with non-collinear magnetization, on the basis of which we obtain the energy spectrum and the Berry curvature. The analysis of topological indices makes it possible to construct a topological phase diagram depending on the parameters of the system and the degree of non-collinearity. For topologically different regions of the diagram, we describe the edge electronic states on the side face of the film. In addition, we investigate the spectrum of one-dimensional states on the domain wall separating domains with the opposite canting angle. We also discuss the results obtained and the experimental situation in thin films of the MnBi$_2$Te$_4$ compound.