Ginzburg-Landau theory for the time-dependent phase field in a two-dimensional d-wave superconductor

We derive a finite temperature time-dependent effective theory for the phas e theta of the pairing field, which is appropriate for a 2D conducting elec tron system with non-retarded d-wave attraction. As for s-wave pairing the effective action contains terms with Landau damping, but their structure ap pears 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 t he d-wave pairing does not have the same direction as the non-interacting F ermi velocity VF. We show that for the d-wave pairing the Landau terms have a linear low temperature dependence and in contrast to the s-wave case are important for all finite temperatures. (C) 2001 Elsevier Science B.V. All rights reserved.