Theory of Josephson effects in iron-based multi-gap superconductor junctions

We revisit the theory for Josephson effects in Josephson junctions with multiple tunneling channels, which can be realized when multi-gap superconductors, e.g., iron-based superconductors or MgB₂ are employed as the electrodes. We mainly re-examine a hetero (multi-band) superconductor- insulator-(single-band)superconductor junction. Deriving an effective Lagrangian density based on the time-dependent Ginzburg-Landau model, we discuss how the relative fluctuations between multiple gaps (i.e., Leggett's excitation modes) and the pairing symmetry modify the Shapiro steps.