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

We study the superconducting phase with two-component order-parameter scenario, such as d(x2-y2) +e(i theta)s(alpha), where alpha=xy,x(2)+y(2). We show that in absence of orthorhombocity, the usual d(x2-y2) does not mix with usual s(x2+y2) symmetry gap in an anisotropic band structure. But the s(xy) symmetry does mix with the usual d-wave symmetry for theta=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 d(x2)-(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 xi, which could be even/odd multiples of lattice spacing, leads to predominant sld-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. [S0163-1829(99)12333-6].