Unconventional band structure for a periodically gated surface of a three-dimensional topological insulator

The surface states of the three-dimensional (3D) topological insulators are described by a two-dimensional (2D) massless dirac equation. A gate-voltage-induced one-dimensional potential barrier on such surfaces creates a discrete bound state in the forbidden region outside the dirac cone. Even for a single barrier it is shown that such a bound state can create an electrostatic analogue of Shubnikov de Haas oscillation which can be experimentally observed for relatively smaller size samples. However, when these surface states are exposed to a periodic arrangement of such gate-voltage-induced potential barriers, the band structure of the same was significantly modified. This is expected to significantly alter the properties of the macroscopic system. We also suggest that, within suitable limits, the system may offer ways to control electron spin electrostatically, which may be practically useful.