The bilayer nickelate La₃Ni₂O₇, a member of the Ruddlesden–Popper series, has recently garnered significant attention due to its superconductivity under high pressure (above 14 GPa) with a transition temperature of approximately 80 K ^[1]. Its unique bilayer structure results in an electronic configuration significantly distinct from those observed in cuprates and infinite-layer nickelates. Consequently, understanding its correlated electronic structure and superconducting mechanism has emerged as a topic of major scientific importance. Recent experimental observations have further identified the coexistence of charge and spin density wave orders in La₃Ni₂O₇, suggesting a complex interplay among various competing electronic phases and superconductivity.
In this work, we investigate the charge order in La₃Ni₂O₇ using a low-energy effective model that explicitly includes the Ni-e_g orbitals. By employing a combined density functional theory and dynamical mean-field theory (DFT+DMFT) framework, we systematically explore the impact of the nearest-neighbor Coulomb interaction V on charge ordering and electronic correlation effects, with nonlocal interactions treated at the Hartree approximation level. Our computational methodology features a newly developed tensor-network impurity solver utilizing a natural-orbital basis and complex-time evolution, facilitating effcient and precise evaluations of the Green’s function on the real-frequency axis.
Our analysis reveals that for interaction strengths below a critical value (V ≤ V_c1 ≈ 0.46 eV), the system maintains sublattice symmetry, resulting in minimal changes to the spectral function. Several high-energy fine structures identified within the Hubbard bands correspond to remnants of atomic multiplet excitations, allowing extraction of effective Hubbard parameters. When V > V_c1, the sublattice symmetry breaks, and the system transitions into a charge-ordered state. Spectral features evolve systematically with increasing charge order, providing a clear benchmark to quantitatively assess the degree of charge disproportionation against experimental data. The quasiparticle weight Z exhibits a nonmonotonic behavior with increasing V , reaching a minimum near V ≈ 0.60 eV in the more populated sublattice as it approaches half-filling. Upon further increasing the interaction beyond V_c2 ≈ 0.63 eV, the system becomes fully charge polarized, characterized by one sublattice becoming nearly empty and the other approaching three-quarter filling.
These findings underscore the critical role of nonlocal Coulomb interactions in driving charge disproportionation and tuning electronic correlations, thereby offering fresh insights into the low-energy ordering phenomena of bilayer nickelates.