On the origin of two-dimensional electron gas states at the surface of topological insulators

The ab initio calculations of the electronic structure in the bulk and at the (0001) surface of narrow-band Bi$_2$Se$_3$, Sb$_2$Te$_3$, Sb$_2$STe$_2$, and Sb$_2$SeTe$_2$ semiconductors have been performed. It has been shown that ternary compounds Sb$_2$STe$_2$ and Sb$_2$SeTe$_2$, as well as the previously known compounds Bi$_2$Se$_3$ and Sb$_2$Te$_3$, are three-dimensional topological insulators. The influence of the subsurface van der Waals gap expansion on the surface electronic structure of these compounds has been analyzed. It has been shown that this expansion leads to the formation of new (trivial) surface states, namely a parabolic state in the conduction band and an M-shaped state in the valence band. These results explain the phenomena discovered recently in photoemission experiments and reveal the nature of new states that are caused by the adsorption of atoms on the surfaces of the layered topological insulators.