Theoretical studies on the observation of the low-frequency plasma oscillation and its coupling with the carlson-goldman mode in dirty quasi-two-dimensional superconductors

The plasma oscillation in a superconductor is investigated for the case when the plasma energy is smaller than the superconducting gap. We show that the plasma energy has a temperature dependence in dirty superconductors. When the strength of the impurity scattering exceeds a critical value, the plasma disappears at the transition temperature (Formula presented) as observed in high-(Formula presented) cuprates (Formula presented) We also study the coupling of the plasma with the Carlson-Goldman (CG) mode in a dirty superconductor. A pole analysis show that the coupling occurs just below (Formula presented) However, even in this situation, we find that two different modelike peak structures can be still observed in the spectra of the density-density correlation function (Formula presented) and the structure function of the pair field susceptibility (Formula presented) The peak in (Formula presented) is located at a finite energy at (Formula presented) corresponding to the low-frequency plasma, while the CG mode with a linear dispersion is found in (Formula presented)