Gap formation in helical edge states with magnetic impurities

Helical edge states appear at the surface of two-dimensional topological insulators and are characterized by spin up traveling in one direction and the spin down traveling in the opposite direction. Such states are protected by time-reversal symmetry and no backscattering due to scalar impurities can occur. However, magnetic impurities break time-reversal symmetry and lead to backscattering. Often their presence is unintentional, but in some cases they are introduced into the sample to open up gaps in the spectrum. We investigate the influence of random impurities on helical edge states, specifically how the gap behaves in the realistic case of impurities having both a magnetic and a scalar component. It turns out that for a fixed magnetic contribution the gap closes when either the scalar component is increased, or Fermi velocity is decreased. We compare diagrammatic techniques in the self-consistent Born approximation to numerical calculations, which yields good agreement. For experimentally relevant parameters we find that even moderate scalar components can be quite detrimental for the gap formation.