Level statistics inside the vortex of a superconductor and symplectic random matrix theory in an external source

Details Level statistics inside the vortex of a superconductor and symplectic random matrix theory in an external source Level statistics inside the vortex of a superconductor and symplectic random matrix theory in an external source

1999-02-03

arxiv.org/abs/cond-mat/9902037v1

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

34 pages, Revtex

Scientific paper

10.1103/PhysRevB.60.3589

In the core of the vortex of a superconductor, energy levels appear inside the gap. We discuss here through a random matrix approach how these levels are broadened by impurities. It is first shown that the level statistics is governed by an ensemble consisting of a symplectic random potential added to a non-random matrix. A generalization of previous work on the unitary ensemble in the presence of an external source (which relied on the Itzykson-Zuber integral) is discussed for this symplectic case through the formalism introduced by Harish-Chandra and Duistermaat-Heckman. This leads to explicit formulae for the density of states and for the correlation functions, which describe the cross-over from the clean to the dirty limits.

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