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

Daijiro Tobe·Mahito Kohmoto·Masatoshi Sato·Yong-Shi Wu
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Abstract

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.

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Daijiro Tobe, Mahito Kohmoto, Masatoshi Sato, Yong-Shi Wu. 2007-05-19. Distribution of spectral-flow gaps in the Rashba model with disorder: a new universality. https://doi.org/10.1103/physrevb.75.245203

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