Perpendicular electric field induced competing $s^\pm$- and $d$-wave pairings in La$_3$Ni$_2$O$_7$ thin film
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$_7$ thin film, we investigated the imbalanced two-orbital bilayer Hubbard model with a layer potential bias using dynamical cluster quantum Monte Carlo calculations. Focusing on the pairing symmetry evolution with the potential bias between layers for the undoped, hole-doped, and electron-doped regimes, we found that the $s^\pm$-wave pairing, originating from the $d_{z^2}$ orbital at high temperature regime as well as $d_{x^2-y^2}$ orbital at lower temperatures, is suppressed by the potential bias; while a possible pairing symmetry transition from $s^\pm$-wave to $d$-wave pairing occurs, driven by the interlayer orbital mismatch and the transfer of electrons into the $d_{x^2-y^2}$ orbitals. 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.