Orthogonality Catastrophe for Vortices in d-Wave Superconductors

Abstract

The dynamics of magnetic vortices in the mixed state of d-wave superconductors is affected by interaction with quasiparticles near the gap nodes. We study this effect by computing the overlap of the ground state wave functions of the nodal quasiparticles in a two-dimensional d-wave superconductor as the ground state changes in response to the motion of the vortex. We find that the overlap is strongly suppressed. This orthogonality catastrophe is specific to a half-quantum vortex and disappears in the case of a doubly-quantized vortex. This implies strong inhibition of the motion of half-quantum vortices. The results allow us to develop a simple description of the quantum vortex creep at low temperatures.