Orbital-selective electron correlations in high-$T_{\rm c}$ bilayer nickelates: from a global phase diagram to implications for spectroscopy

Motivated by the high temperature superconductivity observed in the bilayer nickelate La$_3$Ni$_2$O$_7$ and the spectroscopic evidences of strong electron correlations in this compound, we address the role of its multiorbital electron correlations by proposing a global phase diagram of a bilayer two-orbital Hubbard model. We find a Mott transition developing at half filling, and identify strong orbital selectivity when the system is at the physical electron count. The orbital selectivity is manifested in the formation of interlayer spin singlets between electrons in the $z^2$ orbitals. These features lead to a strong renormalization of the electronic band structure while sustaining a sizable splitting between the bonding and antibonding $z^2$ bands. The proposed orbital-selective correlations naturally explain a series of features as observed in the angular resolved photoemission spectroscopy (ARPES) and optical conductivity measurements in La$_3$Ni$_2$O$_7$. Our results provide a basis to understand both the normal state and the high temperature superconductivity of multilayer nickelates and thereby elucidate correlated superconductivity in general.