Perpendicular electric field induced $s^{\pm }$-wave to $d$-wave superconducting transition in thin film La${}_3$Ni${}_2$O${}_7$

Inspired by the possibility that superconducting properties may be altered by applying a perpendicular electric field in the Ruddlesden-Popper (RP) bilayer nickelate La${}_3$Ni${}_2$O${}_7$, we investigated the imbalanced two-orbital bilayer Hubbard model using dynamical cluster quantum Monte Carlo calculations. Focusing on the pairing symmetries induced by the electric field and their evolution with field strength in the undoped, hole-doped, and electron-doped regimes, we found that the $s^{\pm }$-wave pairing originating from the $d_{z^2}$ orbital is suppressed; while a pairing symmetry transition from $s^{\pm }$-wave to $d$-wave pairing occurs, driven by the interlayer $d_{z^2}$ orbital mismatch and the transfer of electrons into the $d_{x^2-y^2}$ orbital under the applied electric field. Intriguingly, the $d$-wave pairing arising from the $d_{x^2-y^2}$ orbital exhibits dome-like behavior with the electric field. Our large-scale many-body calculations align with the previous expectation from weak-coupling methods and provide further insight into the superconducting mechanism in RP nickelates.