Intrinsic anomalous Hall effect on the surface of a magnetic semiconductor with the strong Rashba effect

In this paper, we theoretically study how electron scattering on domain walls modifies the anomalous transverse conductivity on the surface of a magnetic semiconductor with a strong Rashba effect. The band structure of such a semiconductor, characterized by a nontrivial Berry curvature, determines the occurrence of a one-dimensional resonant state on the magnetic domain wall in a local exchange gap. Under relatively weak exchange splitting, the resonant state has linear dispersion with small spectral broadening and has the property of chirality. It is shown that the presence of a pair of parallel domain walls on the surface can have a measurable physical consequence: an additional almost half-quantized contribution to the anomalous Hall effect. The surface of the BiTeI polar semiconductor doped with transition metal atoms is a suitable material platform for detecting such a contribution.