Ambegaokar-Baratoff relations of Josephson critical current in heterojunctions with multi-gap superconductors

TL;DR

This paper extends the Ambegaokar-Baratoff relation to multi-gap superconductor Josephson junctions, providing a theoretical bound on the critical current that helps identify pairing symmetries in iron-based superconductors.

Contribution

It derives a generalized relation for multi-channel SIS Josephson junctions and applies it to iron-based superconductors to determine pairing symmetry based on critical current measurements.

Findings

The derived bound distinguishes between ±s-wave and s-wave pairing symmetries.

Temperature dependence of $I_c R_n$ reveals differences in gap functions.

The relation aids in identifying pairing symmetry in iron-pnictide superconductors.

Abstract

An extension of the Ambegaokar-Baratoff relation to a superconductor-insulator-superconductor (SIS) Josephson junction with multiple tunneling channels is derived. Appling the resultant relation to a SIS Josephson junction formed by an iron-based (five-band) and a single-band Bardeen-Cooper-Schrieffer (BCS) type superconductors, a theoretical bound of the Josephson critical current ($I_{\rm c}$) multiplied by the resistance of the junction ($R_{\rm n}$) is given. We reveal that such a bound is useful for identifying the pairing symmetry of iron-pnictide superconductors. One finds that if a measured value of $I_{\rm c}R_{\rm n}$ is smaller than the bound then the symmetry is $\pm s$-wave, and otherwise $s$-wave without any sign changes. In addition, we stress that temperature dependence of $I_{\rm c}R_{\rm n}$ is sensitive to the difference of the gap functions from the BCS type gap formula in the above heterojunction.