Effective Hamiltonian and dynamics of edge states in two-dimensional topological insulators under magnetic fields

TL;DR

This paper develops an effective Hamiltonian theory to analyze how magnetic fields affect edge states in 2D topological insulators, impacting their transport properties and electron dynamics.

Contribution

It introduces an analytical framework linking magnetic field-induced gaps to system parameters and studies electron transmission and motion in inhomogeneous potentials.

Findings

Magnetic fields open a gap in edge state spectrum, affecting backscattering.

The theory explains changes in resistance observed in HgTe quantum wells.

Analytical solutions for electron transmission and dynamics in potential barriers.

Abstract

The magnetic field opens a gap in the edge state spectrum of two-dimensional topological insulators thereby destroying protection of these states against backscattering. To relate properties of this gap to parameters of the system and to study dynamics of electrons in edge states in the presence of inhomogeneous potentials, the effective Hamiltonian theory is developed. Using this analytical theory, quantum-mechanical problems of edge-state electron transmission through potential steps and barriers, and of motion in constant electric field are considered. The influence of magnetic field on the resistance of two-dimensional topological insulators based on HgTe quantum wells is discussed together with comparison to experimental data.