Superconducting symmetry of three-dimensional $t$-$J$ model on simple cubic lattice

TL;DR

This study investigates the superconducting symmetry of a 3D $t$-$J$ model on a simple cubic lattice, revealing a transition from isotropic pairing with phase shifts to a 2D d-wave state as anisotropy increases.

Contribution

It introduces a tunable anisotropic parameter in the 3D $t$-$J$ model and analyzes the resulting superconducting symmetries using renormalized mean field theory.

Findings

Isotropic case shows phase-shifted pairing parameters in three directions.

Suppression of coupling in the z direction favors 2D d-wave pairing.

Transition occurs when anisotropic rate drops below 0.75.

Abstract

Motivated by the finding of nearly isotropic superconductivity in $\mathrm{(Ba,K)Fe_2As_2}$, we use renormalized mean field theory to investigated the $t$-$J$ model on three-dimensional simple cubic lattice. A tunable anisotropic parameter is introduced to dictate the coupling on $z$ direction. The symmetry of the superconducting order is studied in detail. Calculation shows that for the isotropic case, pairing parameters on the three perpendicular directions have ${2/3}\pi$ phase shift to each other. However, when the interaction on $z$ direction is suppressed, the corresponding amplitude of the pairing parameter decreases rapidly, furthermore, two-dimensional d-wave state pairing is favored when the anisotropic rate less than 0.75.