Low-temperature Josephson current peak in junctions withd-wave order parameters

Abstract

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 $\sqrt{T}{\mathrm{T}}_{c}$ and its height is ${I}_{c}{R}_{n}=\ensuremath{\pi}\ensuremath{\Delta}/e\sqrt{T}$. 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 $T{\mathrm{T}}_{c}$ and a height ${I}_{c}{R}_{n}=\ensuremath{\pi}\ensuremath{\Delta}/e$. 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.