Linearity of the edge states energy spectrum in the 2D topological insulator

Abstract

Linearity of the topological insulator edge state spectrum plays the crucial role for various transport phenomena. The previous studies found that this linearity exists near the spectrum crossing point, but did not determine how perfect the linearity is. The purpose of the present study is to answer this question in various edge states models. We examine Volkov and Pankratov (VP) model [1] for the Dirac Hamiltonian and the model of [2,3] (BHZ1) for the Bernevig, Hughes and Zhang (BHZ) Hamiltonian [4] with zero boundary conditions. It is found that both models yield ideally linear edge states. In the BHZ1 model the linearity is conserved up to the spectrum ending points corresponding to the tangency of the edge spectrum with the boundary of 2D states. In contrast, the model of[5] (BHZ2) with mixed boundary conditions for BHZ Hamiltonian and the 2D tight-binding (TB) model from [4] yield weak non-linearity.

5 pages, 4 figures

References in corpus (5)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Nonlocal edge state transport in the quantum spin Hall state
• Finite size effects of helical edge states in HgTe/CdTe quantum wells
• Boundary Conditions and Surface States Spectra in Topological Insulators

Cited by in corpus (9)

• Microwave absorption in a 2D topological insulators with a developed network of edge states
• Conductivity of a two-dimensional HgTe layer near the critical width: The role of developed edge states network and random mixture of $p$- and $n$-domains
• Edge capacitance of a 2D topological insulator
• Edge absorption and pure spin current in 2D topological insulator in the Volkov-Pankratov model
• Exact solution for many-body Hamiltonian of interacting particles with linear spectrum
• Universal transparency and fine band structure near the Dirac point in HgTe quantum wells
• Effects of electron-hole asymmetry on electronic structure of helical edge states in HgTe/HgCdTe quantum wells
• Hard wall edge confinement in 2D topological insulators and the energy of the Dirac Point
• Scattering of Electrons between Edge and Two-Dimensional States of a Two-Dimensional Topological Insulator and the Conductivity of the Topological Insulator Strip in a Metallic State