Finite Temperature Time-Dependent Effective Theory for the Phase Field in two-dimensional d-wave Neutral Superconductor

We derive finite temperature time-dependent effective actions for the phase of the pairing field, which are appropriate for a 2D electron system with both non-retarded d- and s-wave attraction. As for s-wave pairing the d-wave effective action contains terms with Landau damping, but their structure appears to be different from the s-wave case due to the fact that the Landau damping is determined by the quasiparticle group velocity v_{g}, which for d-wave pairing does not have the same direction as the non-interacting Fermi velocity v_{F}. We show that for d-wave pairing the Landau term has a linear low temperature dependence and in contrast to the s-wave case are important for all finite temperatures. A possible experimental observation of the phase excitations is discussed.