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

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.