Ambegaokar-Baratoff relations for Josephson critical current in heterojunctions with multigap superconductors

An extension of the Ambegaokar-Baratoff relation to a superconductor- insulator-superconductor (SIS) Josephson junction with multiple tunneling channels is derived. Applying 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 _c) multiplied by the resistance of the junction (R _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 _c R _n is smaller than the bound then the symmetry is ±s wave, and otherwise s wave without any sign changes. In addition, we stress that temperature dependence of I _c R _n is sensitive to the difference of the gap functions from the BCS type gap formula in the above heterojunction.