Semiclassical Scattering by Edge Imperfections in Topological Insulators in a Magnetic Field

We study the scattering of edge states of 2D topological insulator in the uniform external magnetic field due to edge imperfections, common in realistic 2D topological insulator samples. The external magnetic field breaks time-reversal symmetry, opening the possibility of the scattering of otherwise topologically protected fermionic edge states. The scattering happens to be always an over-barrier event, irrespective of the shape of the edge deformation and magnitude of the magnetic field. We use the advanced Pokrovsky–Khalatnikov semiclassical approach, which allows us to obtain analytically both the main exponential and pre-exponential factors of the scattering amplitude for wide classes of analytic deformation profiles.