Model Hamiltonian for topological insulators
Model Hamiltonian for topological insulators
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拓扑绝缘体的哈密顿模型
DOI：
10.1103/physrevb.82.045122
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发表时间：
2010-07-26
影响因子：
3.7
通讯作者：
Zhang, Shou-Cheng
中科院分区：
文献类型：
--
作者：
Liu, Chao-Xing;Qi, Xiao-Liang;Zhang, Shou-Cheng
本文给出了Bi（2）Se（3）族材料（Bi（2）Se（3），Bi（2）Te（3）和Sb（2）Te（3））三维拓扑绝缘体模型哈密顿量的全微观推导.我们首先通过分析原子轨道和应用对称性原理给出一个物理图像来理解电子结构。随后，我们给出了完整的微观推导的模型哈密顿量由Zhang等。[Nat.Phys.5，438（2009）]基于对称性原理和k.p微扰理论。考虑了两种不同类型的k（3）项，它们将面内全旋转对称性破坏为三重旋转对称性。导出了拓扑表面态的有效哈密顿量。在外加磁场的存在下，研究了体模型和表面模型，并给出了相应的朗道能级结构。为了更定量地拟合第一原理计算，我们还提出了一个模型哈密顿量，包括八个能带。
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.