Unveiling Hund-coupling-induced correlated metals in two-orbital Hubbard model

Motivated by the recent discovery of superconductivity in infinite-layer nickelates RE$_{1-\delta}$Sr$_\delta$NiO$_2$ (RE$=$Nd, Pr), we study the role of Hund's coupling in a quarter-filled two-orbital Hubbard model which has been on the periphery of the attention. A region of negative effective Coulomb interaction of this simple model is revealed to be differentiated from three- and five-orbital models in their typical Hund's metal active fillings. We identify three different correlated metal regimes, one of which stems from the proximity to a Mott insulator while the other two from effects of Hund's coupling being away from Mottness. This study establishes Hund's metallicity and further a group of metals exhibiting spin-orbital separation in the two-orbital model. Our picture provides a useful insight to the physics of the infinite-layer nickelates as well as serves as a reference frame for two-orbital systems away from half-filling.