Level statistics inside the vortex of a superconductor and symplectic random matrix theory in an external source
Abstract
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.
Cite
@article{arxiv.cond-mat/9902037,
title = {Level statistics inside the vortex of a superconductor and symplectic random matrix theory in an external source},
author = {E. Brezin and S. Hikami and A. I. Larkin},
journal= {arXiv preprint arXiv:cond-mat/9902037},
year = {2009}
}
Comments
34 pages, Revtex