Effective action approach to the Leggett's mode in two-band   superconductors
  We investigate a collective excitation (Leggett's mode) corresponding to small fluctuations of the relative phase of two condensates in two-band superconductor using the effective ``phase only'' action. We consider the possibility of observing Leggett's mode in MgB$_2$ superconductor and conclude that for the known at present values of the two-band model parameters for MgB$_2$ Leggett's mode arises above the two-particle threshold. 
S.G. Sharapov, V.P. Gusynin, H. Beck