Large Thermoelectric Effects and Inelastic Scattering in Unconventional Superconductors

The thermoelectric coefficient $\eta(T)$ in unconventional superconductors is enhanced below $T_c$ by intermediate strength impurity scattering that is intrinsically particle-hole asymmetric. We compute $\eta(T)$ for a strong-coupling d-wave superconductor and investigate the effects of inelastic scattering originating from electron-boson interactions. We show that $\eta(T)$ is severely suppressed at temperatures just below $T_c$ by a particle-hole symmetric inelastic scattering rate. At lower temperatures inelastic scattering is frozen out and $\eta(T)$ recovers and regains its large amplitude. In the limit $T\to 0$, we have $\eta(T)\sim \eta_{0} T+{\cal O}[T^3]$, where the slope $\eta_{0}$ contains information about the Drude plasma frequency, the details of impurity scattering, and the change in effective mass by electron-boson interactions. In this limit $\eta(T)$ can be used as a probe, complementary to the universal heat and charge conductivities, in investigations of the nature of nodal quasiparticles.