Interplay between spin-singlet and spin-triplet order parameters in a model of an anisotropic superconductor with cuprate planes

Abstract

Model of a two-dimensional anisotropic superconductor with a relatively wide, partially filled conduction band is considered. Attractive nearest neighbor interaction with the amplitude V1, and on-site interaction (with the amplitude V0) taken either as repulsive or attractive are included in the model, along with the tight-binding dispersion relation implying singularities in the density of states. The analytic study is based on the conformal transformation method, which can be regarded as an extension of the Van Hove Scenario, plausible for anisotropic systems such as high-Tc cuprates. Employing the Fourier harmonics as a complete and orthogonal basis for irreducible representations of the cuprate plane symmetry group (C4v), the symmetry of the superconducting order parameter is identified for various values of the model parameters. A wide range of parameters η = 2t1/t0 (the ratio of the second and the first nearest neighbor hopping integrals) and n (the carrier concentration) is studied. The obtained diagrams allow one to identify and mark the areas of stability for the superconducting spin-singlet s- and d-wave and the spin-triplet p-wave order parameters. In particular the problem of coexistence of the s-, p- and d-wave order parameters is addressed and solved for selected values of the ratio V0/V1. A possible island of stability of the d-wave order parameter in the s-wave order parameter environment for a relatively strong on-site interaction is revealed. The triple points, around which the s-, d-, and p-wave order parameters coexist, are identified on the diagrams. It is shown that results of the calculations performed for the two-dimensional tight-binding band model are dissimilar with some obtained within the standard BCS-type approximation. The influence of the on-site interaction on the stability of the s-wave order parameter is explained in detail. The developed and widely illustrated formalism can be easily applied to some more composed models.