Localization problem of electronic states in a two-dimensional quantum spin Hall system (QSH - a symplectic model with a non-trivial topological structure) is studied by the transfer matrix method. The phase diagram in the plane of energy and disorder strength is exposed, and demonstrates "levitation" and "pair-annihilation" of the domains of extended states analogous to that of the integer quantum Hall system. The critical exponent ν for the divergence of the localization length is estimated as ν≅1.6 which is distinct from both exponents pertaining to the conventional symplectic and the unitary quantum Hall systems. This strongly suggests a different universality class related to the non-trivial topology of the QSH system.
@article{arxiv.cond-mat/0605510,
title = {Localization in a quantum spin Hall system},
author = {Masaru Onoda and Yshai Avishai and Naoto Nagaosa},
journal= {arXiv preprint arXiv:cond-mat/0605510},
year = {2015}
}