On the Emergence of Topologically Protected Boundary States in Topological/Normal Insulator Heterostructures

We have performed a systematic investigation of the formation of topologically protected boundary states (TPBS) in topological/normal insulators (TI/NI) heterostructures. Using a recently developed scheme to construct {\it ab-initio} tight-binding Hamiltonian matrices from density functional theory (DFT) calculations, we studied systems of realistic size with high accuracy and control over the relevant parameters such as TI and NI band alignment, NI gap and spin-orbit coupling strength. Our findings point to the existence of an NI critical thickness for the emergence of TPBS and to the importance of the band alignment between the TI and NI for the appearance of the TPBS. We chose Bi$_{2}$Se$_{3}$ as a prototypical case where the topological/normal insulator behavior is modeled by regions with/without spin-orbit coupling. Finally, we validate our approach comparing our model with fully relativistic DFT calculations for TI/NI heterostructures of Bi$_{2}$Se$_{3}$/Sb$_{2}$Se$_{3}$.