Hexagonal warping on optical conductivity of surface states in topological insulator Bi${}_{2}$Te${}_{3}$

Hexagonal warping on optical conductivity of surface states in topological insulator Bi $_{2}$ Te $_{3}$

Zhou Li and J. P. Carbotte

Phys. Rev. B 87, 155416 – Published 15 April 2013

Abstract

Angle-resolved photoemission spectroscopy studies of the protected surface states in the topological insulator Bi $_{2}$ Te $_{3}$ have revealed the existence of an important hexagonal-warping term in its electronic band structure. This term distorts the shape of the Dirac cone from a circle at low energies to a snowflake shape at higher energies. We show that this implies important modifications of the interband optical transitions which no longer provide a constant universal background, as seen in graphene. Rather, the conductivity shows a quasilinear increase with a slightly concave upward bending as energy is increased. Its slope increases with increasing magnitude of the hexagonal distortion, as does the magnitude of the jump at the interband onset. The energy dependence of the density of states is also modified and deviates downward from linear behavior with increasing energy.