Gap functions in anisotropic superconductors

Abstract

In this paper we study superconducting gap functions in planar systems with very different hopping frequencies in the two directions. Allowing the carriers to interact via an isotropic superexchange J (using a two-dimensional t – J model) we calculate the gap function amplitudes by solving the BCS gap equation. The lowering of symmetry induced by such hopping anisotropies results in a mixed symmetry state (of s and d-wave) of the gap function. At smaller anisotropies s-wave pairing dominates the phase diagram at lower densities where we believe our calculations are most accurate. As the system is made progressively more anisotropic, it becomes increasingly difficult to distinguish between the gap function amplitudes corresponding to these two symmetries and in the limit of extreme anisotropy they become identical, with a dramatic increase of the d-wave component. Finally, these gap function amplitudes are used to calculate the thermodynamic properties, e.g. the specific heat, which provides robust support for enhanced pairing correlations in presence of hopping anisotropies.