Model Hamiltonian for topological insulators

Chao Xing Liu, Xiao Liang Qi, Haijun Zhang, Xi Dai, Zhong Fang, Shou Cheng Zhang

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732 Scopus citations


In this paper we give the full microscopic derivation of the model Hamiltonian for the three-dimensional topological insulators in the Bi 2 Se3 family of materials (Bi2 Se3, Bi2 Te3 and Sb2 Te3). 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 [Nat. Phys. 5, 438 (2009)]10.1038/nphys1270 based both on symmetry principles and the k p perturbation theory. Two different types of k3 terms, which break the in-plane full rotation symmetry down to threefold rotation symmetry, are taken into account. An effective Hamiltonian is derived for the topological surface states. Both bulk and surface models are investigated in the presence of an external magnetic field, and the associated Landau level structure is presented. For a more quantitative fitting to the first principle calculations, we also present a model Hamiltonian including eight energy bands.

Original languageEnglish (US)
Article number045122
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number4
StatePublished - Jul 26 2010

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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