Evidence for Anderson-Brinkman-Morel–type state in a heavy-fermion superconductor from ultrasonic attenuation

The ultrasonic attenuation for a superconductor with generalized pairing is calculated via a scalar quasiparticle Boltzmann equation in the relaxation-time approximation, in the hydrodynamic limit. The attenuation follows a power law as a function of temperature T if the gap vanishes at points or lines on the Fermi surface. With an Anderson-Brinkman-Morel–type excitation spectrum, a ${\mathrm{T}}^2$ behavior is obtained for the sound attenuation, which is consistent with the recently measured attenuation for the heavy-fermion system ${\mathrm{UPt}}_3$.