Sensitive dependence of pairing symmetry on Ni-eg crystal field splitting in the nickelate superconductor La3Ni2O7

The discovery of high-temperature superconductivity in La3Ni2O7 under pressure has drawn great attention. However, consensus has not been reached on its pairing symmetry in theory. By combining density-functional-theory (DFT), maximally-localized-Wannier-function, and linearized gap equation with random-phase-approximation, we find that the pairing symmetry of La3Ni2O7 is dxy, if its DFT band structure is accurately reproduced by a downfolded bilayer two-orbital model. More importantly, we reveal that the pairing symmetry of La3Ni2O7 sensitively depends on the crystal field splitting between two Ni-eg orbitals. A slight increase in Ni-eg crystal field splitting alters the pairing symmetry from dxy to s +/-. Such a transition is associated with the change in inverse Fermi velocity and susceptibility, while the shape of Fermi surface remains almost unchanged. Our work highlights the sensitive dependence of pairing symmetry on low-energy electronic structures in multi-orbital superconductors, which calls for care in the downfolding procedure when one calculates their pairing symmetry.