Hexagonal Warping Effects in the Surface States of Topological Insulator Bi$_2$Te$_3$

TL;DR

This paper investigates the hexagonal warping effects on the surface states of the topological insulator Bi$_2$Te$_3$, explaining experimental observations and predicting new signatures in spectroscopic measurements.

Contribution

It introduces an unconventional hexagonal warping term in the surface band structure, providing a theoretical explanation for the observed Fermi surface shape in Bi$_2$Te$_3$.

Findings

Hexagonal warping explains the snow-flake Fermi surface shape.

A single parameter characterizes the warping strength.

Predicted testable signatures in spectroscopic experiments.

Abstract

A single two-dimensinoal Dirac fermion state has been recently observed on the surface of topological insulator Bi$_2$Te$_3$ by angle-resolved photoemission spectroscopy (ARPES). We study the surface band structure using $k \cdot p$ theory and find an unconventional hexagonal warping term, which is the counterpart of cubic Dresselhaus spin-orbit coupling in rhombohedral structures. We show that this hexagonal warping term naturally explains the observed hexagonal snow-flake Fermi surface. The strength of hexagonal warping is characterized by a single parameter, which is extracted from the size of the Fermi surface. We predict a number of testable signatures of hexagonal warping in spectroscopy experiments on Bi$_2$Te$_3$. We also explore the possibility of a spin-density wave due to strong nesting of the Fermi surface.