Semiclassical scattering by edge imperfections in topological insulators under magnetic field

TL;DR

This paper analyzes how edge imperfections in 2D topological insulators under magnetic fields cause scattering of edge states, using semiclassical methods to derive analytical expressions for scattering amplitudes.

Contribution

It introduces a semiclassical approach to analytically calculate scattering amplitudes of edge states in topological insulators with edge imperfections under magnetic fields.

Findings

Scattering is always an over-barrier event regardless of edge shape.

Magnetic field breaks time-reversal symmetry, enabling scattering.

Analytical formulas for scattering amplitude are derived for various edge profiles.

Abstract

We study the scattering of edge states of 2D topological insulator (TI) in the uniform external magnetic field due to edge imperfections, common in realistic 2D TI samples. The external magnetic field breaks time reversal (TR) 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.