Intrinsic spin Hall conductivity in three-dimensional topological insulator/normal insulator heterostructures

Here we study how interface and edge perturbations as well as a size effect can be used to manipulate the transport properties in semiconductor heterostructures where a thin film of three-dimensional topological insulator (TI) is sandwiched by normal insulator (NI) slabs. Within the framework of the NI/TI/NI trilayer model based on a continual scheme, we argue that characteristics of electron states in the TI film (energy spectrum, envelope function profile, the Berry curvature, etc.) are controlled by the film thickness and TI/NI interface potential whose variation can lead to the modification of topological properties of the system. Calculating a spin Hall response for the NI/TI/NI trilayer infinite in the interface plane, we find that a series of quantum transitions between topological insulating phase and trivial band insulator phase can be induced by tuning both the film thickness and the interface potential. We draw in detail the corresponding phase diagram of the NI/TI/NI trilayer, which is controlled by change of the sign of either the hybridization gap or the dispersion parameter. To quantify the edge effect, we formulate a model of the half-infinite in the interface plane NI/TI/NI trilayer, which describes evanescent edge states and provides the necessary conditions under which they exist. It is found that the presence of the in-gap edge states is ambiguously determined by the phase of the TI film. Our findings provide a useful guide in choosing the relevant material parameters to facilitate the observation of quantum spin Hall effect in the TI/NI heterostructures.