  We consider collective excitations in the superfluid state of Fermi condensed
charged gases. The dispersion and damping of collective excitations at nonzero
temperatures are examined, and the coexistence and interaction of different
branches of collective excitations: plasma oscillations, pair-breaking Higgs
modes, and Carlson-Goldman phonon-like excitations are taken into account. The
path integral methods for superfluid Fermi gases and for Coulomb gas are
combined into a unified formalism that extends the Gaussian fluctuation
approximation to account for plasmonic modes. This approximation of Gaussian
pair and density fluctuations is able to describe all branches of collective
excitations existing in a charged superfluid. The spectra of collective
excitations are determined in two ways: from the spectral functions and from
the complex poles of the fluctuation propagator. A resonant avoided crossing of
different modes is shown. It is accompanied by resonant enhancement of the
response provided by the pair-breaking modes due to their interaction with
plasma oscillations. This may facilitate the experimental observation of the
pair-breaking modes.
