A quantitative model for IcR product in d-wave Josephson junctions

We study theoretically the Josephson effect in d-wave superconductor / diffusive normal metal /insulator/ diffusive normal metal/ d-wave superconductor (D/DN/I/DN/D) junctions. This model is aimed to describe practical junctions in high-$T_C$ cuprate superconductors, in which the product of the critical Josephson current ($I_C$) and the normal state resistance ($R$) (the so-called $I_{\rm C}R$ product) is very small compared to the prediction of the standard theory. We show that the $I_{\rm C}R$ product in D/DN/I/DN/D junctions can be much smaller than that in d-wave superconductor / insulator / d-wave superconductor junctions and formulate the conditions necessary to achieve large $I_{\rm C}R$ product in D/DN/I/DN/D junctions. The proposed theory describes the behavior of $I_{\rm C}R$ products quantitatively in high-$T_{\rm C}$ cuprate junctions.