Topological phase transition at the interface of a topological with a conventional insulator

We study the topological states which appear at the interface between a topological insulator (TI) and a conventional insulator (CI) using effective Hamiltonians which accurately describe the band structure of the Bi$_2$Se$_3$ family. Due to the hybridization between the TI and the CI states, the band-gap that appears in the interface Dirac cone decreases and ultimately vanishes by tuning the interface-hopping amplitude or by selecting a CI of appropriate band effective mass. More importantly, we find that a topologically trivial TI slab can be made non-trivial and vice-versa by tuning of such an interface-hopping amplitude or by tuning the CI band effective-mass; namely, a topological phase transition can be induced in such heterostructures indicated by the presence or absence of gapless linear edge modes. We discuss the relevance and realization of our results and conclusions in future experiments.