Abstract
In the frame of $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ method and variational approach for the effective energy functional of a contact between a three-dimensional topological insulator (TI) and normal insulator (NI), we analytically describe the formation of interfacial bound electron states of two types (ordinary and topological) having different spatial distributions and energy spectra. We show that these states appear as a result of the interplay of two factors: hybridization and band bending of the TI and NI electron states near the TI/NI boundary. These results are corroborated by the density functional theory calculations for the exemplar ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}/\mathrm{Zn}\mathrm{Se}$ system.
Highlights
The physical origin, peculiarities and methods of description of bound electron states at the interface formed by a three-dimensional (3D) topological insulator (TI) and normal insulator (NI) are the subject of considerable interest
The ZnSe substrate was modeled by a slab consisting of nine bilayers that is over 20 Ain thickness
Basing on the results obtained, we describe the evolution of the interfacial bound electron states under the influence of charge redistribution and the corresponding band-bending effect near the TI/NI interface
Summary
The physical origin, peculiarities and methods of description of bound electron states at the interface formed by a three-dimensional (3D) topological insulator (TI) and normal insulator (NI) are the subject of considerable interest (see, for example, Refs. [1,2,3] and references therein). The appearance of the bound electron states at the TI/NI contact is due to quantum proximity effect caused by an effective interfacial potential at the boundary between two insulators (semiconductors) with different crystal symmetries, lattice parameters, band gaps, and electron affinities This potential arises from the one-electron hybridization of the TI and NI electron states, as well as redistribution of the charge and spin densities on the both sides of the interface. In such systems, significant electrostatic (Coulomb) potential is induced due to strong charge-density redistribution between TI and NI materials near their contact Since this potential, which has been not considered until now, contains the components of different spatial scales, it may lead to a significant band-bending effect, which is important on the TI (narrow-gap) side of the contact.
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