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Universal level statistics in the presence of Andreev scattering.

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<mark>Journal publication date</mark>22/05/1995
<mark>Journal</mark>Journal of Physics: Condensed Matter
Issue number21
Number of pages18
Pages (from-to)4033-4050
<mark>Original language</mark>English


We study the spectral eigenvalue statistics of tight-binding random matrix ensembles in the presence of Andreev scattering (AS). The nearest-level spacing distribution function is shown to follow a distribution PAS(s) which is distinct from the three well known Wigner-Dyson classes describing disordered "normal" conductors. Numerical results for PAS(s) are obtained for a three-dimensional random tight-binding Hamiltonian and also for a two-dimensional transmission matrix, both including Andreev scattering. The PAS(s) distribution is also analytically reproduced and is shown to coincide with that obtained by folding a GOE metallic spectrum around E=0.