Electronic Transport in Unconventional Superconductors

We investigate the electronic transport coefficients in unconventional superconductors at low temperatures, where charge and heat transport are dominated by electron scattering from random lattice defects. We discuss the features of the pairing symmetry, Fermi surface, and excitation spectrum which are reflected in the low temperature heat transport. For temperatures $k_B T \la \gamma \ll \Delta_0$, where $\gamma$ is the bandwidth of impurity induced Andreev states, certain eigenvalues become {\it universal}, i.e., independent of the impurity concentration and phase shift. Deep in the superconducting phase ($k_B T \la \gamma$) the Wiedemann-Franz law, with Sommerfeld's value of the Lorenz number, is recovered. We compare our results for theoretical models of unconventional superconductivity in high-T$_c$ and heavy fermion superconductors with experiment. Our findings show that impurities are a sensitive probe of the low-energy excitation spectrum, and that the zero-temperature limit of the transport coefficients provides an important test of the order parameter symmetry.