Physica B 312–313 (2002) 51–52 A model of pairing enhanced by stripelike correlations Saurabh Basu a, *, R.J. Gooding a , P.W. Leung b a Department of Physics, Queen’s University, Kingston, Ont., Canada b Department of Physics, University of Science and Technology of Hong Kong, Clear Water Bay, Hong Kong Abstract In this work we describe a simple model of pairing in systems with stripelike hopping anisotropy that mimics one feature of stripe correlations found in numerous transition-metal oxides. Allowing the carriers to interact via Heisenberg superexchange (using a two-dimensional t–J model), we have investigated the effects of such stripelike hopping on the superconducting transition temperature, T c : In general, and most dramatically for d-wave pairing, we find a strong enhancement of T c the greater the degree of hopping anisotropy. Thus, this simple model provides a robust demonstration supporting the conjecture that stripes can indeed augment pairing correlations. r 2002 Elsevier Science B.V. All rights reserved. Keywords: Stripes; Superconductivity theory; Pairing instabilities Strong support for the existence of stripes in high-T c cuprates, and other transition-metal oxides, has been provided by experiments [1]. This leads to the question: Do stripe correlations help or hinder the establishment of superconductivity? In this work we describe a simple model that mimics one aspect of stripe correlations by incorporating an anisotropic hopping Hamiltonian; that is, carriers are expected to be able to move much more readily along the direction of the stripes. Allowing the carriers to interact via Heisenberg superexchange (using a 2d t–J model) we have found exact solutions, in the dilute electron density limit, that demonstrate how stripelike hopping anisotropies can result in dramatic increases in two-electron binding energies [2]. In this report we present results of our recent investigation of the effects of such stripelike hopping anisotropies on T c : In general, and most dramatically for d-wave pairing, we find a strong enhancement of T c the greater the degree of hopping anisotropy. We consider the 2d tight-binding hopping Hamilto- nian given by H hopping ¼ X /i; j S;s t ij ðc w i;s c j;s þ h:c:Þ; where the hopping integral, t ij ; is restricted to be nonzero only when i and j are neighbouring lattice sites. Furthermore, we introduce a hopping anisotropy (r) by specifying t ij ¼ t ðrtÞ for j a neighbour in the x ðyÞ direction; such an anisotropy lowers the symmetry from that of a 2d square lattice to a 2d rectangular lattice. We include interactions between electrons via near-neigh- bour Heisenberg exchange, J ; and an on-site Hubbard repulsion energy, U : The interaction terms become separable according to the operations of the rectangular symmetry group and in the singlet channel consists of an admixture of an on-site s-wave, an extended s-wave, and a d-wave component; here we study the (rectangular) A 1 symmetry superconducting order parameter. In Fig. 1 we show the dependence of T c ; calculated via the nonself-consistent Thouless criterion [3], as a function of free electron density n for U =t ¼ 8and J =t ¼ 1=3 for several values of the anisotropy, viz. r ¼ 0:1; 0:01; 0:001Ffor r ¼ 1 T c is too small to be visible on this plot. (Note that we focus on low densities *Corresponding author. Tel.: +1-613-533-2723; fax: +1- 613-533-6463. E-mail address: saurabh@physics.queensu.ca (S. Basu). 0921-4526/02/$-see front matter r 2002 Elsevier Science B.V. All rights reserved. PII:S0921-4526(01)01556-3