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

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.