Collective excitation modes in multi-band superconductors

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

We extend Leggett's 1966 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, as we find here, is to classify the interband Josephson coupling energy which is the origin of the Leggett's collective modes. Namely, three-band superconductors are shown to accommodate more than one collective modes, which are classified in terms of the "dynamical class" 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.