Effective actions and phase fluctuations in d-wave superconductors

We study effective actions for order-parameter fluctuations at low temperature in layered d-wave superconductors such as the cuprates. The order parameter Lives on the bonds of a square lattice and has two amplitude and two phase modes associated with it. The low-frequency spectral weights for amplitude and relative phase fluctuations is determined and found to be subdominant to quasiparticle contributions. The Goldstone phase mode and its coupling to density fluctuations in;charged systems is treated in a gauge-invariant manner. The Gaussian phase action is used to study both the c-axis Josephson plasmon and the more conventional in-plane plasmon in the cuprates. We go beyond the Gaussian theory by deriving a coarse-grained quantum XY model, which incorporates important cutoff effects overlooked in previous studies. A variational analysis of this effective model shows that in the cuprates, quantum effects of phase fluctuations are important in reducing the zero-temperature superfluid stiffness, but thermal effects are small for T<<T-c.