Re-entrance into insulator phase in two-dimensional disordered system with spin-orbit coupling in the presence of magnetic field

We investigate the localization-delocalization transition of a two-dimensional system with spin-orbit interaction (SOI) in a perpendicular magnetic field. We find that if the system is set between two Landau levels, the increase of SOI strength g can drive the system first from localization state into delocalization state, then back to localization state. Scaling analysis shows that near the transition points the behavior of the correlation length ξ can be well described by function ξ=Aexp(α|gc−g|), with |gc−g| being the distance from the transition point, A being a constant and α being exponent, suggests that Kosterlitz-Thouless nature of the transitions, different from the continuous transition in the absence of the magnetic field.