Evolution of Correlated Electrons in ${\rm La_3Ni_2O_7}$ at Ambient Pressure: a Study of Double-Counting Effect

We employ cluster extension of dynamical mean-field theory (CDMFT) to systematically investigate the impact of double counting corrections on the correlated electronic structure of ${\rm La_3Ni_2O_7}$ under ambient pressure. By adjusting double-counting parameters, while maintaining a fixed Fermi surface, we observe a pronounced orbital-selective density of states change: the $d_{z^2}$ orbital undergoes significant variation near the Fermi level with increasing $E_{dc}^z$, while the $d_{x^2-y^2}$ orbital remains essentially unchanged throughout the entire range. Analysis of renormalization factor show the monotonic dependence with double counting in both $d_{z^2}$ and $d_{x^2-y^2}$ orbital, and it also identifies an optimal double counting window in $d_{z^2}$ orbital aligns with experimental values. We also find the interlayer Matsubara self energy exhibits non-monotonic dependence on $E_{dc}^z$, deviating from theoretical predictions. This anomaly is attributed to the metallization of oxygen-bridged pathways, which disrupts the prerequisite for charge transfer via apical oxygen. Our results establish $E_{dc}$ as a critical control parameter for correlated electronic structure in ${\rm La_3Ni_2O_7}$ and provide a computational framework for resolving orbital-dependent correlation effects in layered materials.