Physica B 378–380 (2006) 430–431 Gap functions in anisotropic superconductors Saurabh Basu à Department of Physics, Indian Institute of Technology Guwahati, North Guwahati, Assam 781039, India 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. r 2006 Elsevier B.V. All rights reserved. PACS: 71.10.Hf; 71.27.+a; 75.30.Mb Keywords: Anisotropy; Superconductivity Motivated by the robust support for stripes in copper- oxide materials [1], we have shown earlier that anisotropic hopping frequencies for carriers that mimics one aspect of stripelike correlations increases superconducting transition temperature, T c [2,3]. In this work, we report calculations of superconducting gap function amplitudes by solving BCS gap equation at finite temperatures. Further we calculate specific heat and both the results indicate towards a strong increase in the d-wave gap amplitude in the limit of extreme hopping anisotropy. We consider a two-dimensional t–J –U model on a square lattice, H ¼ X hi;j i;s t ij ðc y i;s c j ;s þ h:c:Þþ H J þ H U , (1) where t ij are hopping integrals between neighbouring lattice sites i and j . The electrons interact via a nearest- neighbour Heisenberg exchange J and U is the on-site repulsion which in the infinity limit relates to the familiar t–J model. Here we introduce the hopping anisotropy in the following manner, t y ¼ rt x ¼ rt with 0prp1. The lowering of symmetry induced by such anisotropies manifests in the form of a superconducting gap function with a mixed symmetry. We postulate a mixing of the type, D ¼ D s f s ðkÞþ D d f d ðkÞ with f s ðkÞ¼ cos k x þ cos k y and f d ðkÞ¼ cos k x  cos k y as the symmetry factors and D s and D d as the gap amplitudes corresponding to the s and d- wave channels. It has been noted earlier that an additional phase difference between the s and d-wave channels makes no difference in calculating the gap amplitude in the limit of extreme anisotropy (i.e. r ! 0) [3]. With this gap function we solve BCS gap equation at finite temperature D k ¼ X k 0 V kk 0 D k 0 2E k 0 ½1  2f ðE k 0 Þ, (2) alongwith with an electron number conserving equation that controls filling via the chemical potential m, nðm; T Þ¼ 1  1 N X k  k  m E k ½1  2f ðE k Þ, (3) where V kk 0 ¼J ½cosðk x  k 0 x Þþ cosðk y  k 0 y Þ, f ðE k Þ is the Fermi function, E k ’s are the excitation energies defined by, ARTICLE IN PRESS www.elsevier.com/locate/physb 0921-4526/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2006.01.150 à Tel.: +91 361 2582711; fax: +91 361 2690762. E-mail address: saurabh@iitg.ernet.in.