Localization of the helical edge states in quantum spin Hall insulators requires breaking time reversal invariance. In experiments this is naturally implemented by applying a weak magnetic field B. We propse a model based on scattering theory that describes the localization of helical edge states due to coupling to random magnetic fluxes. We find that the localization length is proportional to B^{2} when B is small, and saturates to a constant when B is sufficiently large. We estimate especially the localization length for the HgTe/CdTe quantum wells with known experimental parameters.
@article{arxiv.1207.2400,
title = {Magnetic field induced localization in 2D topological insulators},
author = {Pierre Delplace and Jian Li and Markus Büttiker},
journal= {arXiv preprint arXiv:1207.2400},
year = {2012}
}