Bound states of a short-range defect on the surface of an intrinsic antiferromagnetic topological insulator in a noncollinear phase

The features of electronic states on the surface of an intrinsic antiferromagnetic topological insulator (AFM TI) containing defects are theoretically investigated. Our approach takes into account the role of the electrostatic potential and the variation in the orientation of magnetic moments in the near-surface layers. A change in the spectral characteristics of the surface states under the transformation of magnetization from an equilibrium AFM phase of A-type to a ferromagnetic phase through a noncollinear texture is described. It is shown that in AFM TI with uniaxial anisotropy, an external magnetic field applied along the easy axis can cause a significant modulation of the exchange gap size in the spectrum of surface states and even invert the gap sign. Modeling the single defect effect as a surface potential perturbation over a finite scale, we analytically investigate the formation of a bound state and its behavior depending on the strength of potential and exchange scattering by the defect and the exchange gap size. The energy level of the bound state is demonstrated to experience a sharp shift in the vicinity of the spin-flop transition. The theoretical results obtained allow us to provide a consistent explanation of recent experimental data on scanning tunneling spectroscopy of antisite defects on the surface of the prototype AFM TI MnBi$_2$Te$_4$ in an external magnetic field.