The Mottness and the Anderson localization in bilayer nickelate La$_3$Ni$_2$O$_{7-δ}$

TL;DR

The study addresses how apical-oxygen vacancies in La$_3$Ni$_2$O$_{7-\delta}$ control Mottness and drive Anderson localization, thereby suppressing superconductivity. It develops a bilayer two-orbital tight-binding model for the doped regime ($x=1$) anchored to DFT, uses DMFT to identify a Mott transition in the correlated bilayer, and then treats disorder as a binary mixture of metallic and Mott-insulating states within DCA/TMDCA, supplemented by a Hubbard-I self-energy and BEB formalism. The analysis reveals an Anderson localization transition at $x_c\approx0.4$ ($\delta_c\approx0.2$) that accompanies vacancy-induced insulating behavior, consistent with experiments, and shows that disorder near the superconducting dome can suppress superconductivity via localization. An independent KPM-based check with a band-insulator proxy corroborates the localization threshold, underscoring the crucial role of oxygen stoichiometry in nickelate superconductors and guiding interpretations of recent experimental findings.

Abstract

The oxygen content plays a pivotal role in determining the electronic and superconducting properties of the recently discovered La$_3$Ni$_2$O$_{7-δ}$ superconductors. In this work, we investigate the impact of oxygen vacancies on the insulating behavior of La$_3$Ni$_2$O$_{7-δ}$ across the doping range $δ= 0$ to $0.5$. At $δ= 0.5$, we construct a bilayer two-orbital Hubbard model to describe the system. Using dynamical mean-field theory, we demonstrate that the model captures the characteristics of a bilayer Mott insulator. To explore the effects of disorder within the range $δ= 0$ to $0.5$, we treat the system as a mixture of metallic and Mott insulating phases. By applying the dynamical cluster approximation and the typical medium dynamical cluster approximation, we identify an Anderson localization transition at a critical doping of $δ\sim 0.2$ through the geometric average of the local density of states. This Anderson localization transition is the key reason for the suppression of superconductivity in La$_3$Ni$_2$O$_{7-δ}$. These results provide a quantitative explanation of recent experimental observations and highlight the critical influence of oxygen content on the physical properties of La$_3$Ni$_2$O$_{7-δ}$.

Figures (7)

• Figure 1: The phase diagram of La$_3$Ni$_2$O$_{7-\delta}$ in the region of $\delta=0-0.5$. The variable $x$ represents the additional filling in the $e_g$ orbitals of Ni introduced by the creation of O vacancies in La$_3$Ni$_2$O$_{7-\delta}$, with $x=2\delta$ due to the chemical valence of O is O$^{2-}$. The crystal field splitting is also shown here and the $d_{x^2-y^2}$ orbital is exactly half-filled at $x=1$. We also plot the enlarged bilayer Ni-O octahedral structure for large $x$, in which the corner shared apical pink ball can be regarded as 0.5 oxygen for $x=1$ in VCA. The content of apical oxygen vacancies has a significant impact on superconductivity. The $t$/$b$ indicates the layer index.
• Figure 2: (a) The band structure from DFT calculation. The red and green dots represent the orbital projections of $d_{x^2-y^2}$ and $d_{z^2}$, respectively. (b) The comparison between the DFT calculation (blue lines) and bilayer two-orbital TB model (red lines). We can see the TB bands fit the $e_{g}$ bands very well around the Fermi level.
• Figure 3: (a) The spectral functions $A(\omega)$ for $x=1$ obtained from DMFT calculation based on 4-band model are shown for $U=2$ eV, 4 eV and 5.3 eV, respectively. The $A(\omega)$ gradually evolves from a metallic state into a Mott insulator state, with the clear development of a Mott gap at $U=5.3$ eV. (b) The quasi-particle weight $Z$ at the Fermi level. The Mott transition occurs around $U=5.3$ eV, consistent with the figure (a).
• Figure 4: (a) The density of states of the pure Mott-insulating state obtained by introducing a Hubbard-I self-energy $\Sigma_H(\omega)$ to the La$_3$Ni$_2$O$_{6.5}$ bilayer two-orbital model. (b-d) Comparison of ADOS calculated by DCA and TDOS calculated by TMDCA with various concentration of the Mott states x$_{Mott}$ = 0.2, 0.3, 0.4. Both the DCA and TMDCA calculation use cluster size of $N_c=100$ and 2560 independent disordered realization. The Fermi level is determined by integrating the ADOS according to the doping induced by x$_{Mott}$ and is shifted to zero in all plots.
• Figure S1: (a) The band structure from DFT calculation. (b) The comparison between the first-principles calculation and bilayer single-orbital model. We can see the wannier bands fit the $d_{x^2-y^2}$ bands very well around the Fermi level.