Transition from $s_{\pm}$-wave to $d_{x^{2}-y^{2}}$-wave superconductivity driven by interlayer interaction in the bilayer two-orbital model of La$_3$Ni$_2$O$_7$

Abstract: We utilize the fluctuation-exchange approximation on a bilayer two-orbital model, incorporating $d_{x^2-y^2}$ and $d_{z^2}$ orbitals, to explore potential pairing symmetries in the bilayer nickelate La$3$Ni$_2$O$_7$. Our study particularly examines the impact of interlayer Coulomb interactions. In the absence of these interactions, the superconducting gap exhibits $s{\pm}$-wave symmetry, with predominant intraorbital pairing in the $d_{z^2}$ orbital. As interlayer interactions increase, $s_{\pm}$-wave superconductivity is suppressed, while the superconductivity with a $d_{x^2-y^2}$-wave gap is enhanced, resulting in a transition at a critical interaction strength. This $d_{x^2-y^2}$-wave superconductivity is distinct not only from the $s_{\pm}$-wave superconductivity but also from the intraorbital $d$-wave pairing in cuprate superconductors, as it is dominated by the interlayer pairing between the $d_{x^2-y^2}$ and $d_{z^2}$ orbitals. Additionally, charge fluctuations play a crucial role in driving the transition from $s_{\pm}$ wave to $d_{x^2-y^2}$ wave superconductivity. Our findings indicate that interlayer Coulomb interactions are crucial for understanding the pairing mechanism in La$_3$Ni$_2$O$_7$.