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 $(\overrightarrow{\Omega }0,$ $\overrightarrow{T}0)$ 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.

• Received 16 August 1999

DOI:https://doi.org/10.1103/PhysRevB.62.1270