Impact of nonlocal Coulomb repulsion on superconductivity and density-wave orders in bilayer nickelates

The recent discovery of high-temperature superconductivity in pressurized bilayer nickelate La3Ni2O7 and its thin films has sparked considerable interest in unraveling their pairing mechanisms and correlated electronic states. While earlier theoretical studies have primarily focused on onsite Coulomb interactions, the impact of nonlocal Coulomb repulsion has remained largely unexplored. In this work, we systematically investigate the influence of nonlocal Coulomb interactions on both superconductivity and density-wave instabilities, in the presence of onsite interactions, by employing the functional renormalization group (FRG) approach. We find that the interlayer intra-orbital repulsion suppresses the interlayer intra-orbital s±-wave pairing and spin-density-wave (SDW) order, while promoting a transition to an interlayer inter-orbital $${d}_{{x}^{2}-{y}^{2}}$$-wave pairing state and a mirror-symmetry-breaking charge order. Remarkably, the critical scale of the inter-orbital $${d}_{{x}^{2}-{y}^{2}}$$-wave superconductivity is significantly lower than that of the intra-orbital s±-wave superconductivity, suggesting that the former pairing is unlikely to account for the observed high-Tc superconductivity. In addition, the interlayer inter-orbital repulsion suppresses this $${d}_{{x}^{2}-{y}^{2}}$$-wave pairing but promotes the s±-wave pairing owing to enhanced interlayer charge fluctuations. In addition, the intralayer nearest-neighbor repulsion favors an in-plane charge density wave (CDW) order with wave vector (π, π). Our findings highlight the profound impact of nonlocal Coulomb repulsion and the robustness of interlayer pairing associated with the bilayer structure and the multi-orbital nature, advancing the understanding of the complex correlation effects within bilayer nickelates.