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

Ota, Yukihiro; Nakai, Noriyuki; Nakamura, Hiroki  ; Machida, Masahiko  ; Inotani, Daisuke*; Ohashi, Yoji*; Koyama, Tomio*; Matsumoto, Hideki*

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 () multiplied by the resistance of the junction () 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 is smaller than the bound then the symmetry is -wave, and otherwise -wave without any sign changes. In addition, we stress that temperature dependence of is sensitive to the difference of the gap functions from the BCS type gap formula in the above heterojunction.