Abstract
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 aims 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 ${I}_{C}R$ product) is very small compared to the prediction of the standard theory for clean $d$-wave superconductor/insulator/$d$-wave superconductor (DID) junctions. We show that the ${I}_{C}R$ product in D/DN/I/DN/D junctions can be much smaller than that in DID junctions. The proposed theory describes the behavior of ${I}_{C}R$ products quantitatively in high-${T}_{C}$ cuprate junctions.
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