Theory of ac Josephson effects in multiple tunneling junctions: A probe of $\pm s$-wave in iron-based superconductors

An enormous amount of studies has been devoted to the identification of the pairing symmetry in iron-based superconductors. We show a theory of Josephson junctions with multi-gap superconductors. We focus on a heterotic (multi-band)superconductor- insulator-(one-band)superconductor junction. We derive the Ambegaokar-Baratoff relation. We evaluate a lower bound of $J_{\rm c}R_{\rm n}$ for $s$-wave without sign change, which may correspond to a upper bound for $\pm s$-wave. Next, we discuss how a fluctuation of relative phases between the gaps and the symmetry modify the Shapiro step. Thus, we propose a direct method to identify $\pm s$-wave.