On possible deep subsurface states in topological insulators: The PbBi$_4$Te$_7$ system

Theoretical studies of the bulk and surface electronic structures of PbBi$_4$Te$_7$ are presented. The PbBi$_4$Te$_7$ compound has a layered structure of five-layer (Bi$_2$Te$_3$) and seven-layer (PbBi$_2$Te$_4$) blocks alternating along the hexagonal axis. Analysis of the spin–orbit-induced inversion of the band gap edges indicates that this compound is a three-dimensional topological insulator. The topological properties of this compound are mainly determined by the PbBi2Te4 blocks. The Dirac cone is formed on the PbBi$_4$Te$_7$(0001) surface near the $\bar\Gamma$ point for any block (either Bi$_2$Te$_3$ или PbBi$_2$Te$_4$) forming the surface. It is shown that the Dirac state can be localized not only on the surface but also deeply beneath it.