Low-temperature Josephson current peak in junctions with d -wave order parameters

A low-temperature peak in the critical current of Josephson junctions containing d-wave order parameters (D) was recently found by Barash et al. [Phys. Rev. Lett. 77, 4070 (1996)]. We point out that the height and width of this low-temperature peak is limited by the transmission coefficient T through the insulator (I) separating the two superconductors. In planar DID junctions the width of the Josephson current peak in temperature is √TTc and its height is IcRₙ=πΔ/e√T. In SID junctions, where S is an ordinary s-wave superconductor, the corresponding low-temperature peak in the Josephson current has a width in temperature TTc and a height IcRₙ=πΔ/e. Both the height and width of the low-temperature Josephson current peak follow from the bound Andreev-level spectrum in SID and DID junctions. Interface roughness and suppression of the order parameter near the interface will also affect the height and width of the low-temperature peak.