A rigorous theory based on the Ward-Takahashi (WT) relations originating from U(1) gauge symmetry is presented for the collective phase oscillation modes in multiband superconductors. The existence of the massless Nambu-Goldstone mode in the superconducting state including the time-reversal-symmetry-breaking phase can be rigorously proved by using the WT relations. We also discuss the approximations in calculating the phase oscillation modes in systems with an interaction causing the gap renormalization.
ASJC Scopus subject areas
- Physics and Astronomy(all)