Pairing symmetry and long-range pair potential in a weak-coupling theory of superconductivity

Abstract

We study the superconducting phase with two-component order-parameter scenario, such as dx2−y2+eiθsα, where α=xy,x2+y2. We show that in absence of orthorhombocity, the usual dx2−y2 does not mix with usual sx2+y2 symmetry gap in an anisotropic band structure. But the sxy symmetry does mix with the usual d-wave symmetry for θ=0. The d-wave symmetry with higher harmonics present in it also mixes with higher-order extended s-wave symmetry. The required pair potential to obtain higher anisotropic dx2−y2 and extended s-wave symmetries is derived by considering longer ranged two-body attractive potential in the spirit of tight-binding lattice. We demonstrate that the dominant pairing symmetry changes drastically from d- to s-like as the attractive pair potential is obtained from longer ranged interaction. More specifically, a typical length scale of interaction ξ, which could be even/odd multiples of lattice spacing, leads to predominant s/d-wave symmetry. The role of long-range interaction on pairing symmetry has further been emphasized by studying the typical interplay in the temperature dependencies of these higher-order d- and s-wave pairing symmetries.

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