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We apply both analytical and ab-initio methods to explore heterostructurescomposed of a threedimensional topological insulator (3D TI) and an ultrathinnormal insulator (NI) overlayer as a proof ground for the principles of thetopological phase engineering. Using the continual model of a semi-infinite 3DTI we study the surface potential (SP) effect caused by an attached ultrathinlayer of 3D NI on the formation of topological bound states at the interface.The results reveal that spatial profile and spectrum of these near-surfacestates strongly depend on both the sign and strength of the SP. Using ab-initioband structure calculations to take materials specificity into account, weinvestigate the NI/TI heterostructures formed by a single tetradymite-typequintuple or septuple layer block and the 3D TI substrate. The analyticalcontinuum theory results relate the near-surface state evolution with the SPvariation and are in good qualitative agreement with those obtained fromdensity-functional theory (DFT) calculations. We predict also the appearance ofthe quasi-topological bound state on the 3D NI surface caused by a local bandgap inversion induced by an overlayer.

Modeling Near-Surface Bound Electron States in Three-Dimensional Topological Insulator: Analytical and Numerical Approaches