On the Plasma Oscillation in Superconductivity

The plasma mode in the superconducting state is studied within the random phase approximation. It is proved that the plasma oscillation in the limit of zero momentum (g) is not affected by the superconductivity. This statement itself has been obtained so far under some special conditions where energies of the plasma frequency and the superconducting order parameter are much different. In this paper, we clarify that it holds true at all temperatures irrespective of (1) the magnitude of the plasma frequency, (2) the symmetry of the order parameter, and (3) details of the system, e.g., dimensionality and the layered structure. We also show that the plasma sum-rule is satisfied even in the superconducting state, which states that the spectrum of the density-density correlation function in the limit q → 0 is dominated by the plasma mode only Although the phase fluctuation of the order parameter couples with the charge one, the collective phase oscillation, so-called the Carlson-Goldman mode, does not contribute to the spectrum of the density-density correlation function in this limit.