Boundary Conditions and Surface States Spectra in Topological Insulators

Abstract

We study spectra of surface states in 2D topological insulators (TIs) based on HgTe/(Hg,Cd)Te quantum wells and 3D Bi${}_2$Se${}_3$-type compounds by constructing a class of feasible time-reversal invariant boundary conditions (BCs) for an effective $\mathbf{k}\mathbf{p}$-Hamiltonian and a tight-binding model of the topological insulators. The BCs contain some phenomenological parameters which implicitly depend on both bulk Hamiltonian parameters and crystal potential behavior near the crystal surface. Space symmetry reduces the number of the boundary parameters to four real parameters in the 2D case and three in the 3D case. We found that the boundary parameters may strongly affect not only an energy spectrum but even the very existence of these states inside the bulk gap near the Brillouin zone center. Nevertheless, we reveal in frames of the tight-binding model that when surface states do not exist in the bulk gap in the Brillouin zone center they cross the gap in other points of the Brillouin zone in agreement with the bulk-boundary correspondence.

Title, abstract, and introduction are updated; published version

References in corpus (5)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Topological Insulators with Inversion Symmetry
• Finite size effects of helical edge states in HgTe/CdTe quantum wells
• Interface Contributions to the Spin-Orbit Interaction Parameters of Electrons at the (001) GaAs/AlGaAs Interface
• Modeling Near-Surface Bound Electron States in Three-Dimensional Topological Insulator: Analytical and Numerical Approaches

Cited by in corpus (5)

• High-frequency nonlinear transport and photogalvanic effects in two-dimensional topological insulators
• Surface States of a System of Dirac Fermions: A Minimal Model
• Fermi arcs formation in Weyl semimetals: the key role of intervalley interaction
• Edge absorption and pure spin current in 2D topological insulator in the Volkov-Pankratov model
• Conservation of chirality at a junction between two Weyl semimetals