Interplay between Hubbard interaction and charge transfer energy in three-orbital Emery model: implication on cuprates and nickelates

TL;DR

The paper addresses how the interplay between onsite Cu interaction $U_{dd}$ and charge-transfer energy $ε_p$ shapes the normal-state physics of the three-orbital Emery model, with relevance to cuprates and nickelates. It employs determinant quantum Monte Carlo (DQMC) with maximum-entropy analytic continuation to compute orbital occupancies, LDOS, $A_eta(oldsymbol{k},ω)$, and spin correlations across doping and energy scales on an $8×8$ lattice. The key results show a possible Zhang-Rice singlet (ZRS) breakdown in heavily overdoped regimes, a suppression of the pseudogap at large $ε_p$, and an optimal $ε_p$ (approximately 4) that maximizes antiferromagnetic correlations near half-filling; these findings emphasize the pivotal role of $ε_p$ in determining spectral and magnetic properties and suggest the Emery model as a unified framework for cuprates and infinite-layer nickelates. The work also notes that the sign problem is milder in the charge-transfer-insulator regime, opening a path to further exploration of multi-orbital physics in these materials.

Abstract

We use the numerically unbiased determinant quantum Monte Carlo (DQMC) method to systematically investigate the three-orbital Emery model in the normal state in a wide range of local interactions, charge transfer energy, and doping levels. We focus on the influence of the onsite Hubbard $U_{dd}$ and the charge transfer energy scale $ε_p$ on the electronic properties via the orbital occupancies, local moments, spin correlations, and spectral properties. Rich features of the orbital-resolved local and momentum-dependent spectra are revealed to associate with the possible Zhang-Rice singlet (ZRS) breakdown reflected by the peak splitting near the Fermi level in the heavily overdoped regime. Moreover, the pseudogap features at a small charge transfer energy scale (relevant to cuprates) are shown to diminish at larger $ε_p$, which implies the weakening or absence of the pseudogap in the infinite-layer nickelates. Besides, an optimal value of $ε_p$ is identified for maximizing the antiferromagnetic (AFM) spin correlations. Our large-scale simulations provide new insights on the well-established Emery model, particularly in the regime of heavily overdoped and/or large charge transfer energy scale.

Figures (10)

• Figure 1: A schematic illustration of a Cu-$d_{x^2-y^2}$ orbital and its four nearest-neighbor O-$p_{x/y}$ orbitals. Red (blue) color indicates positive (negative) phase factor. The unit cell is outlined by the dashed box. The phase convention of the hopping parameters is defined in the hole language.
• Figure 2: Total filling $\langle n_{\mathrm{tot}} \rangle$ versus the chemical potential $\mu$ for fixed $\epsilon_p=$ 3.0 (a) and 6.0 (b) with varying $U_{dd}$. The dashed line represents half-filling, with the hole-doped and electron-doped regions labeled above and below the line respectively.
• Figure 3: The hole density on Cu orbital $\langle n_{\mathrm{Cu}} \rangle$ versus that on O orbital $\langle n_{\mathrm{O}} \rangle$ with $\epsilon_p$ or $U_{dd}$ being fixed. The dashed line denotes the half-filling $\langle n_{\text{tot}} \rangle = 1.0$ case. The hole-doped and electron-doped regions are labeled at the upper-right and lower-left sides of the line, respectively. The dotted line indicates $\langle n_{\mathrm{Cu}} \rangle = \langle n_{\mathrm{O}} \rangle$, i.e. equal occupancies on Cu and O.
• Figure 4: Local density of states (LDOS) as a function of (a, d, e) doping level, (b) $\epsilon_p$, (c) $U_{dd}$, and (f) $\beta$. The varied parameter values are indicated to the right of each panel. The spectra of O orbital is summed over the $x$- and $y$-direction. The orange triangles denote the location of the UHB.
• Figure 5: The orbital-resolved spectral function $A_{\alpha}(\mathbf{k},\omega)$ along the high-symmetry path $\Gamma$-$M$-$X$-$\Gamma$ in the Brillouin zone. Following the discussion of LDOS, $U_{dd}$ is kept constant at 6.0 as well. The spectral weight of O at $\Gamma$ point is truncated for better clarity. Owing to the momentum-space anisotropy of the spectral function, the O spectrum is obtained by summing the contributions along the $x$- and $y$-directions.