Universality in Transport Processes of Unconventional Superconductors

TL;DR

This paper demonstrates that certain low-temperature transport coefficients in specific unconventional superconductors are universal, unaffected by impurities, and depend on the order parameter symmetry, revealing new insights into their fundamental properties.

Contribution

It establishes the conditions under which transport coefficients become universal and shows how impurity studies can differentiate order parameter symmetries in unconventional superconductors.

Findings

Transport coefficients are universal at low temperatures.

Universality depends on order parameter symmetry.

Impurity concentration studies distinguish order parameter types.

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.