
Physics 2002
Ultrasonic Attenuation in Clean dWave SuperconductorsDOI: 10.1016/S09214534(02)022736 Abstract: We calculate the low temperature longitudinal ultrasonic attenuation rate $\alpha_S$ in clean dwave superconductors. We consider the contribution of previously ignored processes involving the excitation of a pair of quasiholes or quasiparticles. These processes, which are forbidden by energy conservation in conventional swave superconductors, have a finite phase space in dwave superconductors due to the presence of nodes in the gap which give rise to soft lowenergy electronic excitations. We find the contribution to $\alpha_S$ from these processes to be proportional to $T$ in the regime $k_B T\ll Qv_{\Delta} \ll \Delta_0$,(ultralow temperature regime) and to be proportional to 1/T in the region $Qv_F \ll k_BT \ll \Delta_0$, (low temperature regime) where ${\bf Q}$ is the ultrasound wavevector and $\Delta_0$ is the maximum gap amplitude. We explicitly evaluate these terms, for parameters appropriate to the cuprates, for ${\bf Q}$ along the nodal and the antinodal directions and compare it with the contribution from processes considered earlier(I.Vekhter et al {\it Phys. Rev.}{\bf B59}, 7123(1999)). In the ultralow temperature regime, the processes considered by us make a contribution which is smaller by about a factor of 10 for ${\bf Q}$ along the nodal direction, while along the antinodal direction it is larger by a factor of 100 or so. In the low temperature regime on the other hand the contribution made by these terms is small. However taken together with the original terms we describe a possible way to evaluate the parameter $v_F/v_\Delta$.
