Correlation-renormalized spin-fluctuation pairing and the stabilization of $s_{\pm }$ superconductivity in pressurized La${}_3$Ni${}_2$O${}_7$

The superconducting gap symmetry of pressurized La${}_3$Ni${}_2$O${}_7$ remains unsettled because conventional weak-coupling calculations often place the system close to competing sign-changing $s$- and $d$-wave instabilities. Using the four-orbital Wannier Hamiltonian of Xia et al., we combine single-site two-orbital dynamical mean-field theory (DMFT) with a self-energy-renormalized random-phase approximation (RPA). The central step is to replace the bare particle-hole bubble $G_0{G}_0$ of ordinary RPA by a $G_{\mathrm{D}\mathrm{M}\mathrm{F}\mathrm{T}}{G}_{\mathrm{D}\mathrm{M}\mathrm{F}\mathrm{T}}$ bubble, while keeping the same residual Slater–Kanamori interaction vertices. In the bare RPA benchmark, the leading pairing eigenvalue belongs to the $B_{2g}$ $d_{xy}$ channel. Once the DMFT self-energy is included, the hierarchy is reversed: the $A_{1g}$ sign-changing $s_{\pm }$ state becomes dominant, the $B_{1g}$ $d_{x^2-y^2}$ channel is subleading, and the original $B_{2g}$ instability is strongly suppressed. Pocket-pair decomposition and orbital-resolved susceptibilities show that the reversal originates from orbital-selective renormalization of the $d_{3z^2-r^2}$ sector, which filters the $\gamma$-pocket scattering processes that stabilize $d_{xy}$ pairing in bare RPA while preserving distributed inter-pocket processes favorable to $s_{\pm }$ pairing. As an independent two-particle validation, we further compute the static spin susceptibility using the dual Bethe–Salpeter equation with the local DMFT vertex. The resulting susceptibility retains a broad finite-momentum magnetic response and is weak near $\mathrm{\Gamma }$, strengthening the spin-fluctuation background for the correlation-stabilized $s_{\pm }$ state. Our results demonstrate that strong correlations are not a secondary correction in La${}_3$Ni${}_2$O${}_7$: an appropriate treatment of correlation-renormalized quasiparticles is essential for predicting the superconducting pairing symmetry.