Effect of doping on the electronic structure, orbital-dependent renormalizations, and magnetic correlations in bilayer La$_3$Ni$_2$O$_7$

Abstract

Using the DFT+dynamical mean-field theory approach we study the effects of electronic correlations and doping on the normal state electronic structure of the double-layer nickelate superconductor La$_3$Ni$_2$O$_7$ under pressure. In agreement with experiments, we obtain significant orbital-dependent quasiparticle renormalizations of the Ni $x^2-y^2$ and $3z^2-r^2$ bands, accompanied by incoherence (bad metal behavior) of the $3z^2-r^2$ states, caused by the proximity of the Ni $3d$ states to orbital-dependent localization. Our results demonstrate a sensitive, non-monotonic dependence of $m^*/m$ on doping, with a remarkable, by about 20\%, increase for the Ni $x^2-y^2$ orbitals upon electron doping $x \sim 0.2$ (per Ni ion), implying a significant enhancement of orbital-dependent correlations with oxygen deficiency in LNO. We observe a reconstruction of the low-energy electronic structure of LNO upon doping above $x\sim -0.3$ and 0.2. It is associated with the Lifshitz transition, with a crossover to a self-doping regime characterized by partial occupation of the La $5d$ bands (upon an electron doping $x>0.2$). Our analysis of the static magnetic susceptibility $\chi({\bf q})$ suggests the possible formation of the spin and charge density wave stripes, implying strong spin and charge correlations in LNO. We show that this behavor is associated with suppression of the N\'eel AFM ordering of the Ni$^{2+}$ ions upon hole doping. Interestingly, upon a moderate electron doping of the Ni$^{2.5+}$ ions, we find a significant enhancement of the strength of in-plane spin fluctuations. We note a close resembles of our results to those for the bilayer Hubbard model, which shows the boosting of superconductivity as one of the two electron bands approaches the Lifshitz transition. Our results suggest that spin and charge stripe fluctuations play a key role in pressure-driven superconductivity in LNO.