Effective actions and phase fluctuations in d-wave superconductors

We study effective actions for order-parameter fluctuations at low temperat ure in layered d-wave superconductors such as the cuprates. The order param eter Lives on the bonds of a square lattice and has two amplitude and two p hase modes associated with it. The low-frequency spectral weights for ampli tude and relative phase fluctuations is determined and found to be subdomin ant to quasiparticle contributions. The Goldstone phase mode and its coupli ng to density fluctuations in;charged systems is treated in a gauge-invaria nt manner. The Gaussian phase action is used to study both the c-axis Josep hson plasmon and the more conventional in-plane plasmon in the cuprates. We go beyond the Gaussian theory by deriving a coarse-grained quantum XY mode l, which incorporates important cutoff effects overlooked in previous studi es. A variational analysis of this effective model shows that in the cuprat es, quantum effects of phase fluctuations are important in reducing the zer o-temperature superfluid stiffness, but thermal effects are small for T<<T- c.