Impurity-induced quasiparticle transport and universal-limit Wiedemann-Franz violation ind-wave superconductors

Abstract

Due to the node structure of the gap in a d-wave superconductor, the presence of impurities generates a finite density of quasiparticle excitations at zero temperature. Since these impurity-induced quasiparticles are both generated and scattered by impurities, prior calculations indicate a universal limit $(\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Omega}}0,$ $\stackrel{\ensuremath{\rightarrow}}{T}0)$ where the transport coefficients obtain scattering-independent values, depending only on the velocity anisotropy ${v}_{f}{/v}_{2}.$ We improve upon prior results, including the contributions of vertex corrections and Fermi-liquid corrections in our calculations of universal-limit electrical, thermal, and spin conductivity. We find that while vertex corrections modify electrical conductivity and Fermi-liquid corrections renormalize both electrical and spin conductivity, only thermal conductivity maintains its universal value, independent of impurity scattering or Fermi-liquid interactions. Hence, low-temperature thermal conductivity measurements provide the most direct means of obtaining the velocity anisotropy for high-${T}_{c}$ cuprate superconductors.