Universality in Transport Processes of Unconventional Superconductors

Abstract

We show that some of the low temperature transport coefficients (e.g., electrical and thermal conductivities, viscosity and sound attenuation) are {\it universal}, i.e., independent of the impurity concentration and phase shift for specific classes of unconventional superconductors. The existence of a universal limit depends on the symmetry of the order parameter and is achieved at low temperatures $k_B T \ll \gamma \ll \Delta_0$, where $\gamma$ is the bandwidth of the impurity induced Andreev bound states. The density of states is finite at zero energy and leads to the re-appearance of the Wiedemann-Franz law deep in the superconducting phase for $k_B T \ll \gamma$. Our findings also show that impurity concentration studies at low temperatures can distinguish between different order parameter symmetries.