Leggett's modes in multi-band superconductivity

Ota, Yukihiro; Machida, Masahiko  ; Koyama, Tomio*; Aoki, Hideo*

One important way to characterize multi-band superconductors should be to look at their collective excitation modes, which are expected to reflect the broken gauge symmetry that involves multi-bands. Here we extend Leggett's analysis for a massive out-of-phase collective mode coexisting with the Nambu-Goldstone mode in two-band superconductors to the case where there are three or more bands. Crucial is to classify the inter-band Josephson coupling energy which is the origin of the Leggett's collective modes. Three-band superconductors are shown to accommodate more than one collective modes, which are classified in terms of the "dynamicalclass" that distinguishes the parity of the inter-band Josephson current. The mass of the multiple Leggett's modes is then shown to dramatically depend on the class. We expect that the present prediction can be tested in the iron-based superconductor (with a gap function involving three bands).