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

Abstract

Motivated by the finding of nearly isotropic superconductivity in $(\mathrm{Ba},\mathrm{K})\mathrm{F}{\mathrm{e}}_2\mathrm{A}{\mathrm{s}}_2$, 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.

4 pages, 4 figures