Distribution of spectral-flow gaps in the Rashba model with disorder: a new universality

We report a study of disordered electron systems with spin-orbit coupling on a cylinder using methods of random matrix ensembles. With a threading flux turned on, the single particle levels will generally avoid, rather than cross, each other. Our numerical study of the level-avoiding gaps in the disordered Rashba model demonstrates that the normalized gap distribution is of a universal form, independent of the random strength and the system size. For small gaps it exhibits a linear behavior, while for large gaps it decays exponentially. A framework based on matrix mechanical models is suggested, and is verified to reproduce the universal linear behavior at small gaps. Thus we propose to use the distribution of the spectral-flow gaps associated with flux insertion as a new way to characterize 2d random systems with spin-orbit coupling. The relevance and qualitative implications for spin (Hall) transport are also addressed.