Anomalous Hall and spin Hall conductivities in three-dimensional ferromagnetic topological insulator/normal insulator heterostructures

In this letter we theoretically demonstrate how an interface perturbation and size effect can be used to manipulate the transport properties of semiconductor heterostructures composed of a thin film of a three-dimensional topological insulator (TI) doped with magnetic impurities and sandwiched between topologically normal insulators. In the framework of a continual scheme, we argue that electron states of the TI film are strongly dominated by its thickness and magnetization as well as by an interface potential whose variation can lead to the modification of topological properties of the heterostructure. This opens diverse possibilities to efficiently tune intrinsic Hall conductivity in the system. We calculate a phase diagram of the heterostructure, which demonstrates a series of quantum transitions between distinct regimes of conductivity. We derive the anomalous Hall conductivity and the spin Hall conductivity dependences on the chemical potential. Applicability conditions of the used approach are also discussed.We acknowledge partial support from Saint Petersburg State University (project No. 15.61.202.2015) and Russian Foundation of Basic Researches (grant No. 16-02-00024).Peer reviewe