Conductance of d-wave superconductor/normal metal/d-wave superconductor junctions

We develop a theory of the low-temperature conductance of superconductor/normal metal/superconductor junctions in which the superconductors have d-wave pairing symmetry. We show that at low temperatures the conductance of the junction is determined by the inelastic relaxation time of quasiparticles in the bulk of d-wave superconductors, $G_{DND}\propto \sqrt{\tau^ {(d)}_{\epsilon}}$. Thus it greatly exceeds the conductance of the normal metal part of the junction, which is controlled by the elastic mean free path. This dependence of $G_{DND}$ on the inelastic relaxation time should be contrasted with that of the low-temperature conductance of the junction in the case of the s- wave superconductor leads, $G_{SNS}$. In the latter case the conductance is proportional to the first power of the inelastic electron relaxation time in the normal metal part of the junction, $G_{SNS}\propto \tau_{\epsilon}^{(n)}$ [1]. \newline [1] S. V. Lempitskii, Sov. Phys. JETP {\bf{58}}, 624 (1983); U. Gunsenheimer and A. D. Zaikin, Phys. Rev. B{\bf{50}}, 6317 (1994); F. Zhou and B. Spivak, JETP Lett. {\bf{65}}, 369 (1997).