Non-Fermi liquid and antiferromagnetic correlations with hole doping in the bilayer two-orbital Hubbard model of La$_3$Ni$_2$O$_7$ at zero temperature

TL;DR

This study uses advanced computational methods to explore the phase transitions and magnetic correlations in a bilayer Hubbard model of La3Ni2O7, revealing a sequence of electronic phases and the impact of doping and pressure on magnetic and superconducting tendencies.

Contribution

It provides a detailed zero-temperature phase diagram of the bilayer two-orbital Hubbard model for La3Ni2O7, highlighting the emergence of non-Fermi liquid behavior and magnetic correlations with doping.

Findings

Sequential phase transitions from Mott insulator to Fermi liquid with doping.

Identification of non-Fermi liquid phase with Hund spin correlations.

Doping and pressure influence magnetic correlations and potential superconductivity.

Abstract

High-$T_c$ superconductivity (SC) was recently found in the bilayer material La$_3$Ni$_2$O$_7$ (La327) under high pressures. We study the bilayer two-orbital Hubbard model derived from the band structure of the La327. The model is solved by cluster dynamical mean-field theory (CDMFT) with natural orbitals renormalization group (NORG) as impurity solver at zero temperature, considering only normal states. With hole doping, we have observed sequentially the Mott insulator (Mott), pseudogap (PG), non-Fermi liquid (NFL), and Fermi liquid (FL) phases, with quantum correlations decreasing. The ground state of the La327 is in the NFL phase with Hund spin correlation, which transmits the Ni-$3d_{z^2}$ ($z$) orbital inter-layer AFM correlation to the Ni-$3d_{x^2-y^2}$ orbitals. When the $\sigma$-bonding state of the $z$ orbitals ($z+$) is no longer fully filled, the inter-layer antiferromagnetic (AFM) correlations weaken rapidly. At low pressures, the fully filled $z+$ band supports a strong inter-layer AFM correlations, potentially favoring short-range spin density wave (SDW) and suppressing SC. Hole doping at low pressures may achieve a similar effect to high pressures, under which the $z+$ band intersects with the Fermi level, and consequently the spin correlations weaken remarkably, potentially suppressing the possible short-range SDW and favoring SC.