  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.
