We apply both analytical and ab-initio methods to explore heterostructures composed of a 3D topological insulator (3D TI) and an ultrathin normal insulator (NI) overlayer as a proving ground for the principles of topological phase engineering. Using the continual model of a semi-infinite 3D TI we study the surface potential (SP) effect caused by an attached ultrathin layer of 3D NI on the formation of topological bound states at the interface. The results reveal that the spatial profile and spectrum of these near-surface states strongly depend on both the sign and the strength of the SP. Using ab-initio band structure calculations to take the specificity of the materials into account, we investigate the NI/TI heterostructures formed by a single tetradymite-type quintuple or septuple layer block and the 3D TI substrate. The analytical continuum theory results relate the near-surface state evolution with the SP variation and are in good qualitative agreement with those obtained from density-functional theory (DFT) calculations. We also predict the appearance of the quasi-topological bound state on the 3D NI surface caused by a local band gap inversion induced by an overlayer.
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