Effective action approach and Carlson-Goldman mode in d-wave superconductors

We theoretically investigate the Carlson-Goldman (CG) mode in two-dimensional clean d-wave superconductors using the effective 'phase-only' action formalism. In conventional s-wave superconductors, it is known that the CG mode is observed as a peak in the structure factor of the pair susceptibility S(Ω,K) only just below the transition temperature Tc and only in dirty systems. On the other hand, our analytical results support the statement by Ohashi and Takada [Phys. Rev. B 62, 5971 (2000)] that in d-wave superconductors the CG mode can exist in clean systems down to much lower temperatures, T≅0.1Tc. We also consider the manifestations of the CG mode in the density-density and current-current correlators and discuss the gauge independence of the obtained results