Random-matrix ensembles in p-wave vortices

TL;DR

This paper predicts two new random-matrix ensembles, B and DIII-odd, in disordered p-wave superconductor vortices, based on symmetry analysis of Bogoliubov-deGennes equations, highlighting zero-energy quasiparticle levels.

Contribution

It explicitly derives the symmetry classes of vortex states in p-wave superconductors, identifying the conditions for realizing the new ensembles B and DIII-odd.

Findings

Identification of B and DIII-odd ensembles in vortex spectra.

Zero-energy quasiparticle levels are characteristic of these classes.

Disorder mainly arises from order parameter distortions around impurities.

Abstract

In disordered vortices in p-wave superconductors the two new random-matrix ensembles may be realized: B and DIII-odd (of so(2N+1) and so(4N+2)/u(2N+1) matrices respectively). We predict these ensembles from an explicit analysis of the symmetries of Bogoliubov-deGennes equations in three examples of vortices with different p-wave order parameters. A characteristic feature of the novel symmetry classes is a quasiparticle level at zero energy. Class B is realized when the time-reversal symmetry is broken, and class DIII-odd when the time-reversal symmetry is preserved. We also suggest that the main contribution to disordering the vortex spectrum comes from the distortion of the order parameter around impurities.