Eur. Phys. J. B 59, 141-150 (2007)
https://doi.org/10.1140/epjb/e2007-00275-3

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

Max-Planck-Institut für Festkörperforschung, Heisenbergstrasse 1, 70569 Stuttgart, Germany

Corresponding author: ^a r.zeyher@fkf.mpg.de

Received: 4 April 2007
Revised: 9 July 2007
Published online: 10 October 2007

Abstract

Phase fluctuations of a d-wave superconducting order parameter are theoretically studied in the context of high-T_c cuprates. We consider an extended t-J model describing electrons in a layer which also contains long-range Coulomb interactions. The constraint of having at most singly occupied sites is enforced by an additional Hubbard term. The Heisenberg interaction is decoupled by a d-wave order parameter in the particle-particle channel. Assuming first that the equilibrium state has long-range phase order, the effective action 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 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 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 to the case of interacting electrons, is explicitly gauge invariant, and avoids problematic singular gauge transformations.