Effective action for phase fluctuations in d-wave superconductors near a Mott transition

Abstract

Phase fluctuations of a d-wave superconducting order parameter are theoretically studied in the context of high-T${}_c$ cuprates. We consider the $t-J$ model describing layered compounds, where the Heisenberg interaction is decoupled by a d-wave order parameter in the particle-particle channel. Assuming first that the equilibirum state has long-range phase order, the effective action ${\mathcal{S}}_{eff}$ is derived perturbatively for small fluctuations within a path integral formalism, in the presence of the Coulomb and Hubbard interaction terms. In a second step, a more general derivation of ${\mathcal{S}}_{eff}$ is performed in terms of a gradient expansion which only assumes that the gradients of the order parameter are small whereas the value of the phase may be large. We show that in the phase-only approximation the resulting ${\mathcal{S}}_{eff}$ reduces in leading order in the field gradients to the perturbative one which thus allows to treat also the case without long-range phase order or vortices. Our result generalizes previous expressions for ${\mathcal{S}}_{eff}$ to the case of interacting electrons, is explicitly gauge invariant, and avoids problematic singular gauge transformations.

11 pages, 4 figures, REVTeX

References in corpus (1)

• Quantum criticality of d-wave quasiparticles and superconducting phase fluctuations