Model Hamiltonian for Topological Insulators

TL;DR

This paper provides a detailed microscopic derivation of the model Hamiltonian for three-dimensional topological insulators in the Bi2Se3 family, including symmetry analysis, surface state modeling, and magnetic field effects.

Contribution

It offers a comprehensive derivation of the topological insulator Hamiltonian based on symmetry and perturbation theory, including new terms and an extended model with eight bands.

Findings

Derived the full microscopic Hamiltonian for Bi2Se3 family.

Analyzed surface states and Landau levels under magnetic fields.

Presented an extended model with eight energy bands for better accuracy.

Abstract

In this paper we give the full microscopic derivation of the model Hamiltonian for the three dimensional topological insulators in the $Bi_2Se_3$ family of materials ($Bi_2Se_3$, $Bi_2Te_3$ and $Sb_2Te_3$). We first give a physical picture to understand the electronic structure by analyzing atomic orbitals and applying symmetry principles. Subsequently, we give the full microscopic derivation of the model Hamiltonian introduced by Zhang {\it et al} [\onlinecite{zhang2009}] based both on symmetry principles and the ${\bf k}\cdot{\bf p}$ perturbation theory. Two different types of $k^3$ terms, which break the in-plane full rotation symmetry down to three fold rotation symmetry, are taken into account. Effective Hamiltonian is derived for the topological surface states. Both the bulk and the surface models are investigated in the presence of an external magnetic field, and the associated Landau level structure is presented. For more quantitative fitting to the first principle calculations, we also present a new model Hamiltonian including eight energy bands.