Model Hamiltonian for topological insulators

In this paper we give the full microscopic derivation of the model Hamiltonian for the three-dimensional topological insulators in the ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ family of materials (${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$, ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$ and ${\mathrm{Sb}}_{2}{\mathrm{Te}}_{3}$). 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 $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ perturbation theory. Two different types of ${k}^{3}$…