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

TL;DR

This study demonstrates that the double-counting correction $E_{dc}$ is a pivotal control parameter for correlated electrons in ${\rm La_3Ni_2O_7}$ at ambient pressure. Using CDMFT on an 11-band Hubbard model with a $2\times 2$ NiO cluster, the authors show orbital-selective spectral changes, with $d_{z^2}$ being highly sensitive to $E_{dc}$ while $d_{x^2-y^2}$ remains robust, and identify an optimal $E_{dc}^z$ window around $10.2$–$10.5$ eV where the renormalization matches experimental tendencies. They also reveal a non-monotonic interlayer self-energy due to metallization of oxygen-bridged pathways, emphasizing that conventional double-counting schemes may fail to capture orbital-resolved correlations in layered nickelates. The work provides a framework for resolving orbital-dependent correlation effects in similar layered materials and highlights the importance of carefully selecting $E_{dc}$ when modeling nickelates and related systems.

Abstract

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.

Figures (4)

• Figure 1: The evolution of Fermi surface with decreasing the double-counting energies $E_{dc}^z$. Here the Fermi surface profile is manually adjusted to match that from the ARPES resultARPES, which leads to only one independent parameter among ($E_{dc}^z$, $E_{dc}^x$, $\mu_{pz}$), see main text for details.
• Figure 2: Evolution of DOS as a function of $E_{dc}^z$.
• Figure 3: (a) Electron densities as a function of $E_{dc}^z$. (b) Renormalization factor $Z^{-1}$ for $d_{z^2}$ and $d_{x^2-y^2}$ orbitals as a function of $E_{dc}^z$. Inset show the quantity $\epsilon_{pz}-\mu_{pz}-\epsilon_{loc}^z$ as a function of $E_{dc}^z$, which is proportional to the charge-transfer energy $E_{dp}$ and can be regarded as a reference.
• Figure 4: (a),(b) show the interlayer term in $d_{z^2}$ of Matsubara self-energy varying with double counting values in ($E_{dc}^z,E_{dc}^x$). Data points sharing identical self-energy values in panels (a) and (b) correspond to the same parameter set.