Interlayer interactions in $\text{La}_3\text{Ni}_2\text{O}_7$ under pressure: from $s^{\pm}$ to $d_{xy}$-wave superconductivity

We investigate the role of \emph{interlayer} interaction terms in the competition between different superconducting gap symmetries in the bilayer nickelate $\text{La}_3\text{Ni}_2\text{O}_7$ under high pressure. We study a two-layer, two-orbital electron model that encompasses both intra- and interlayer Coulomb interaction terms within the matrix random-phase approximation. We find that interlayer interactions favor a $d_{xy}$-wave superconducting pairing symmetry over the $s^{\pm}$-wave symmetry, which has been found to prevail when interlayer interactions are disregarded. Moreover, our findings indicate that interlayer interactions enhance the interorbital pairing, incorporating contributions from all three electron pockets, arising from both $d_{3z^2-r^2}$ and $d_{x^2-y^2}$ orbital character, resulting in nodes within the gap function (not present in the $s^{\pm}$-wave state) and consequently favoring the $d_{xy}$-wave pairing.