Transport in vortex state of d-wave superconductors at zero temperature: Wiedemann-Franz violation

TL;DR

This paper demonstrates that the Wiedemann-Franz law is violated at zero temperature in the vortex state of a d-wave superconductor due to impurity scattering and supercurrent effects, with implications for thermal and electrical conductivities.

Contribution

It introduces a semiclassical approach accounting for Doppler shifts and vortex scattering to analyze conductivity violations in d-wave superconductors at zero temperature.

Findings

Wiedemann-Franz law is violated at zero temperature in the vortex state.

Vertex corrections to electric conductivity become negligible at high magnetic fields.

Thermal conductivity corrections remain insignificant regardless of magnetic field.

Abstract

We show that the Wiedemann-Franz law is violated at zero temperature in the vortex state of a d-wave BCS superconductor with isotropic impurity scattering. We use a semiclassical approach to include the Doppler shift experienced by the quasiparticles due to the circulating supercurrents and consider as well the Andreev scattering from an array of vortices assumed to be randomly distributed. We also show that the vertex corrections to the electric conductivity, which can be large when there is significant anisotropy in the impurity scattering, become unimportant as the magnetic field is increased. For the thermal conductivity, the corrections remain negligible as in the absence of a magnetic field.