Universal distribution of spectral-flow gaps in the Rashba model with disorder

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 the use of the distribution of the spectral-flow gaps associated with flux insertion as a way to characterize two-dimensional random systems with spin-orbit coupling. The relevance and qualitative implications for spin (Hall) transport are also addressed.