  Gapless boundary modes at the interface between topologically distinct
regions are one of the most salient manifestations of topology in physics.
Metallic boundary states of time-reversal-invariant topological insulators
(TIs), a realization of topological order in condensed matter, have been of
much interest not only due to such a fundamental nature, but also due to their
practical significance. These boundary states are immune to backscattering and
localization owing to their topological origin, thereby opening up the
possibility to tailor them for potential uses in spintronics and quantum
computing. The heterojunction between a TI and a normal insulator (NI) is a
representative playground for exploring such a topologically protected metallic
boundary state and expected to constitute a building block for future
electronic and spintronic solid-state devices based on TIs. Here, we report a
first-principles study of two experimentally realized lattice-matched
heterojunctions between TIs and NIs, Bi$_2$Se$_3$(0001)/InP(111) and
Bi$_2$Te$_3$(0001)/BaF$_2$(111). We evaluate the band offsets at these
interfaces from many-body perturbation theory within the $GW$ approximation as
well as density-functional theory. Furthermore, we investigate the topological
interface states, demonstrating that at these lattice-matched heterointerfaces
they are strictly localized and their helical spin textures are as well
preserved as those at the vacuum-facing surfaces. These results taken together
may help in designing devices relying on spin-helical metallic boundary states
of TIs.
