Model Hamiltonian for topological insulators

By Chaoxing Liu, Xiao-Liang Qi, Haijun Zhang, X. Dai, Z. Fang, Shoucheng Zhang. 2010

608 citations recorded by the source corpus.

In this paper we give the full microscopic derivation of the model Hamiltonian for the three-dimensional topological insulators in the Bi(2)Se(3) family of materials (Bi(2)Se(3), Bi(2)Te(3) and Sb(2)Te(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 et al. [Nat. Phys. 5, 438 (2009)] based both on symmetry principles and the k.p perturbation theory. Two different types of k(3) 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.

Subfields: Atomic and Molecular Physics, and Optics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/de8bf073db347c678fc9c0d9c0df542102663474

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In Atomic and Molecular Physics, and Optics

In Materials Chemistry

Citations in the corpus

Topological insulators and superconductors (2010, background): “Interestingly, in another family of QSH insulators, Bi2Se3 and Bi2Te3 thin films (Liu et al., 2010), the conditionGEGH 0 is also satisfied when magnetic impurities such as Cr or Fe are introduced into the system, but for a different physical reason.”
Materials perspective on Casimir and van der Waals interactions (2015, background): “…limit the 2D states, which are topologically protected by symmetry invariance, are described by a helical version of the massless Dirac Hamiltonian (Liu et al., 2010; Zhang et al., 2009) Hsurf = ẑ · (σ × k) , (15) where ẑ is the unit vector perpendicular to the surface (located in the xy-plane),…”