Formation of the magnetic order in three-dimensional topological insulators for the quantum anomalous Hall effect (scientific summary)

The topical problem of realization of the proper transverse conductivity in magnetic heterostructures based on topological insulators has been discussed. Our recent theoretical studies developing a universal approach to analytically simulate the quantum anomalous Hall effect at various ways for introducing a magnetic order into a topological insulator film have been briefly reviewed. Our model involves a consistent description of electronic states of the system, which determine the quantum anomalous Hall effect, with the reduction of the dimension from three-dimensional bulk through two-dimensional interface to one-dimensional edge. This makes it possible to emphasize the particular role of physical boundaries such as interfaces and side faces for spin-dependent transport in heterostructures. A number of new results recently obtained within the proposed approach have been reported. The data of recent experiments with new magnetic materials and structures have been discussed in terms of our theoretical results.