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

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${}_{7-\delta }$.

7 pages, 4 figures and Supplemental Materials