Bulk and interface quantum states of electrons in multi-layer heterostructures wiph topological materials

In this article we describe the bulk and interface quantum states of electrons in multi-layer heterostructures in one dimension, consisting of topological insulators (TIs) and topologically trivial materials. We use and extend an effective four-band continuum Hamiltonian by introducing position dependence to the eight material parameters of the Hamiltonian. We are able to demonstrate complete conduction-valence band mixing in the interface states. We find evidence for topological features of bulk states of multi-layer TI heterostructures, as well as demonstrating both complete and incomplete conduction-valence band inversion at different bulk state energies. We show that the linear k(z) terms in the low-energy Hamiltonian, arising from overlap of p(z) orbitals between different atomic layers in the case of chalcogenides, control the amount of tunneling from TIs to trivial insulators. Finally, we show that the same linear k(z) terms in the low-energy Hamiltonian affect the material's ability to form the localised interface state, and we demonstrate that due to this effect the spin and probability density localisation in a thin film of Sb(2)Te3( )is incomplete. We show that changing the parameter that controls the magnitude of the overlap of p(z) orbitals affects the transport characteristics of the topologically conducting states, with incomplete topological state localisation resulting in increased backscattering.