Gap symmetries from the neighbor coupling in square-lattice superconductors

TL;DR

This paper investigates how the symmetries of superconducting gaps in square-lattice materials are determined by neighbor coupling potentials, providing a unified understanding for both conventional and high-temperature superconductors.

Contribution

It introduces a symmetry-based framework linking gap symmetries to neighbor coupling potentials, supported by numerical demonstrations.

Findings

Neighbor coupling potentials determine gap symmetries.

Both isotropic and anisotropic gaps are possible.

Numerical results confirm the theoretical predictions.

Abstract

The gap symmetries of superconductivity are studied in this work. It is found that the gap symmetries are simply determined by the 4-fold rotational symmetries of the coupling potential on neighbor sites. A local on-site coupling potential results in the on-site pairing with the conventional s-wave symmetry, but a coupling potential between the nearest neighbors or the next-nearest neighbors results in the pairing on neighbor sites with the $s^-$, $d_{x^2-y^2}$, $d_{xy}$, or $s_{x^2y^2}$ gap symmetries. It is proved that both isotropic and anisotropic gap functions are allowed by the 4-fold rotational symmetries of the coupling potential. Finally a numerical computation is performed to demonstrate the gap symmetries. This neighbor coupling provides a unified picture for the gap functions of the conventional and the high Tc superconductivity.