Collective vibrations in superconductors with low carrier density and overlapping energy bands on the Fermi surface

Collective vibrations in two-band superconductors with low carrier densities are studied for the case described by the BCS superconductivity theory and for the case where localized pairs form a Bose condensate (the Schaffroth theory of superconductivity). It is shown that in both cases, there exists an acoustic mode of collective vibrations and an exciton-type collective mode caused by interband electron–electron interactions. For systems with low carrier densities, the frequencies of the collective vibrations are significantly influenced by the mixing of the phase and amplitude fluctuations of the order parameters for different bands.