Doping-driven evolution of pairing symmetry in pressurized La$_3$Ni$_2$O$_7$
We investigate the superconducting pairing symmetry and its doping evolution in pressurized La$_3$Ni$_2$O$_7$. For the undoped compound, the most favorable pairing state is found to be $s_{\pm}$-wave, characterized by sign reversal of the gap functions between the Fermi pockets. A detailed analysis of the pairing interactions reveals that this unconventional state originates from repulsive interactions mediated by the magnetic odd modes of the bilayer nickelate. Upon hole doping, the $γ$ Fermi pocket expands, which amplifies the intrapocket repulsions on this pocket. These repulsions, driven by the magnetic even modes, gradually dominates the pairing interactions and ultimately drive a transition in pairing symmetry from $s_{\pm}$-wave to $d_{xy}$-wave in the heavily hole-doped regime. In stark contrast, the $s_{\pm}$-wave pairing persists under electron doping, even deep into the heavily electron-doped regime where a Lifshitz transition occurs. This finding suggests that the $γ$ Fermi pocket is not essential for the emergence of superconductivity in bilayer nickelates. In fact, the $s_{\pm}$-wave pairing becomes more robust in the absence of the $γ$ pocket, as spin fluctuations are strongly enhanced by the favorable nesting between the $α$ and $β$ pockets --- a condition guaranteed by Luttinger's theorem and the Fermi surface topology. We believe that exploring the doping evolution of superconducting pairing will open a new realm for testing the pairing mechanism in pressurized La$_3$Ni$_2$O$_7$.