Wiedemann-Franz violation in the vortex state of a d-wave superconductor

TL;DR

This paper demonstrates that the Wiedemann-Franz law, which relates thermal and electrical conductivities, is violated in the vortex state of a d-wave superconductor at zero temperature, using a semiclassical approach.

Contribution

It introduces a semiclassical method accounting for Doppler shift and Andreev scattering to analyze conductivity in the vortex state of d-wave superconductors.

Findings

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

Vertex corrections become negligible with strong magnetic fields.

Doppler shift and Andreev scattering significantly affect quasiparticle transport.

Abstract

We show that the Wiedemann-Franz law is violated in the vortex state of a d-wave superconductor at zero temperature. We use a semiclassical approach, which includes the Doppler shift on the quasiparticles as well as the Andreev scattering from a random distribution of vortices. We also show that the vertex corrections to the electrical conductivity due to the anisotropy of impurity scattering become unimportant in the presence of a sufficiently large magnetic field.