Sensitive dependence of pairing symmetry on Ni-e_g 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 the pairing symmetry in theory. By combiningdensity-functional-theory (DFT), maximally-localized-Wannier-function, and linearized gap equation with random-phase-approximation, we find that the pairing symmetry of La₃Ni₂O₇ is d_xy, if its DFT band structure is accurately reproduced in 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-e_g orbitals. A slight increase in the Ni-e_g 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 structure in multi-orbital superconductors, which calls for care in the downfolding procedure when one calculates their pairing symmetry.