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

TL;DR

This paper investigates how oxygen vacancies influence the electronic phases of La$_3$Ni$_2$O$_{7-eta}$, revealing an Anderson localization transition that suppresses superconductivity, using advanced theoretical models and simulations.

Contribution

It introduces a bilayer two-orbital Hubbard model and applies dynamical mean-field theory to explain the localization phenomena in La$_3$Ni$_2$O$_{7-eta}$.

Findings

Identification of an Anderson localization transition at δ ≈ 0.2.

Demonstration that oxygen vacancies induce a transition from metallic to insulating phases.

Explanation of the suppression of superconductivity due to localization effects.

Abstract

The oxygen content plays a pivotal role in determining the electronic and superconducting properties of the recently discovered La$_3$Ni$_2$O$_{7-\delta}$ superconductors. In this work, we investigate the impact of oxygen vacancies on the insulating behavior of La$_3$Ni$_2$O$_{7-\delta}$ across the doping range $\delta = 0$ to $0.5$. At $\delta = 0.5$, 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 $\delta = 0$ 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 $\delta \sim 0.2$ 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$_{7-\delta}$. 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$_{7-\delta}$.