Unconventional band structure for a periodically gated surface of a three dimensional Topological Insulator

TL;DR

This paper investigates how a periodic array of gate-induced potential barriers on a 3D topological insulator surface modifies its band structure, revealing potential for electron spin control and observable quantum oscillations.

Contribution

It introduces the concept of a nontrivially modified band structure due to periodic gating on topological insulator surfaces, suggesting new ways to control electron spin electrostatically.

Findings

Periodic gating alters the surface state band structure.

Bound states can produce observable Shubnikov de Haas oscillations.

Potential for electrostatic control of electron spin.

Abstract

The surface states of the three dimensional (3D) Topological Insulators are described by two-dimensional (2D) massless dirac equation. A gate voltage induced one dimensional potential barrier on such surface creates a discrete bound state in the forbidden region outside the dirac cone. Even for a single barrier it is shown such bound state can create 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 got nontrivially modified. This is expected to significantly alters the properties of macroscopic system. We also suggest that in suitable limit the system may offer ways to control electron spin electrostatically which may be practically useful.