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

TL;DR

This paper investigates how long-range pair potentials influence the pairing symmetry in superconductors, revealing a transition from d-wave to s-wave dominance as the interaction range varies.

Contribution

It introduces a theoretical framework linking longer-ranged attractive interactions to changes in pairing symmetry, including the mixing of different order parameters in anisotropic band structures.

Findings

Long-range interactions can switch the dominant pairing symmetry from d-wave to s-wave.

Mixing of different symmetry components occurs depending on the interaction phase and range.

Temperature dependence of higher-order pairing symmetries is significantly affected by interaction range.

Abstract

We study the superconducting phase with two component order parameter scenario, such as, $d_{x^2-y^2} + e^{i\theta}s_{\alpha}$, where $\alpha = xy, x^2+y^2$. We show, that in absence of orthorhombocity, the usual $d_{x^2-y^2}$ does not mix with usual $s_{x^2+y^2}$ symmetry gap in an anisotropic band structure. But the $s_{xy}$ symmetry does mix with the usual d-wave 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 $d_{x^2-y^2}$ 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 $s/d$ 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.