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

E. Brezin (1) , S. Hikami , A. I. Larkin

1 LPTENS - Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure]

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.

Domaines: Systèmes mésoscopiques et effet Hall quantique [cond-mat.mes-hall]

E. Brezin, S. Hikami, A. I. Larkin. Level statistics inside the vortex of a superconductor and symplectic random matrix theory in an external source. Physical Review B: Condensed Matter and Materials Physics (1998-2015), 1999, 60, pp.3589-3602. ⟨hal-00005190⟩