Relaxation of Hot Quasiparticles in a $d$-Wave Superconductor

Motivated by recent pump-probe experiments we consider the processes by which “hot” quasiparticles produced near the antinodes of a d-wave superconductor can relax. We show that in a large region of momentum space processes which break Cooper pairs are forbidden by energy and momentum conservation. Equilibration then occurs by scattering with thermal quasiparticles: Umklapp scattering is exponentially suppressed at low temperatures, but small-angle scattering leads to power-law behavior. By solving the Boltzmann equation analytically we make detailed predictions for the temperature and intensity dependence of these processes, which we compare with experiment.