LOW-FREQUENCY RESPONSE FUNCTION OF A SUPERCONDUCTOR AT FINITE TEMPERATURE

The full temperature-dependent dielectric function is developed for the superconducting state. The specific case of low-temperature and low-frequency is solved within the Bardeen-Cooper-Schrieffer model potential for the imaginary part ε2(q,Ω). The result is found to give a term proportional to Ω52 for the contribution of the collective excitations, along with the usual Ω term due to quasiparticle excitations. Reference is made to recent work by Ferrell and Schmidt, in which consideration of fluctuations in the phase of the complex order parameter of the superconducting state requires that ε2(q, Ω) increase more rapidly than Ω2 in order for the state to remain stable against these fluctuations. The discrepancy between this result and our work indicates the necessity for considering fluctuations in the magnitude of the order parameter as well as the phase, for a complete investigation of the effects of fluctuations. © 1969 The American Physical Society.