The superconducting properties of a recently proposed phenomenological model for a weakly doped antiferromagnet are analyzed, taking into account fluctuations of the phase of the order parameter. In this model, we assume that the doped charge carriers cannot move out of the antiferromagnetic sublattice in which they were introduced. This case corresponds to free-carrier spectra with the maximum at $\mathbf{k}=(\pm \mathrm{<ruby><rb>\pi </rb><rt>ぱい</rt></ruby>}∕2,\pm \mathrm{<ruby><rb>\pi </rb><rt>ぱい</rt></ruby>}∕2)$, as it was observed in angle-resolved photoemission spectroscopy experiments for some of the cuprates in the insulating state [A. Damascelli et al., Rev. Mod. Phys. 75, 473 (2003)]. The doping dependence of the superconducting gap and the temperature–carrier density phase diagram of the model are studied in the case of the $d_{x^2-y^2}$ pairing symmetry of the order parameter and different values of the model parameters. A possible relevance of the results to experiments on high-temperature superconductors is discussed.

• Received 30 October 2006

DOI:https://doi.org/10.1103/PhysRevB.75.224513