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Phonon attenuation and quasiparticle–phonon energy transfer ind-wave superconductors

We calculate the rate of energy transfer between phonons and quasiparticles that are out of thermal equilibrium in cuprate superconductors at temperatures below the impurity scattering rate. Phonons that give a significant contribution to phonon-quasiparticle energy transfer at millikelvin temperatures have frequencies that extend through the crossover frequency at which sound attenuation deviates from an ω 2 frequency dependence. The crossover frequency for a given phonon depends on the direction of its in-plane momentum because of the anisotropy of the nodal quasiparticle energy dispersion relation. The temperature dependence of the heat transfer rate is thus sensitive to the ratio v f /v 2 , which characterizes the anisotropy of quasiparticle energy at the node. We estimate the magnitude of the heat transfer rate in optimally doped YBa 2 Cu 3 O 6 + λ . We also compare our results for pure d-wave superconductors with measurements of the ultrasonic attenuation in Sr 2 RuO 4 and discuss implications for the gap symmetry in that material.