Random matrix theory and metal–insulator transition in disordered superconductors

Abstract

Level statistics for symmetry class D of random matrix ensembles is investigated. It arises in models of non-interacting quasiparticles in disordered superconductors without time-reversal and spin-rotation invariance. In the metallic regime, the nearest-neighbor spacing distribution (NNSD) reproduces exactly the Wigner surmise for GUE as one should expect in the presence of magnetic field, whereas in the localized regime, level repulsion is supressed. NNSD therefore reflects some basic symmetries of the system while ignoring particle–hole symmetries.