Hund Physics Landscape of Two-Orbital Systems

Motivated by the recent discovery of superconductivity in infinite-layer nickelates RE1−δSrδNiO2 ( RE = Nd , Pr), we study the role of Hund coupling J 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 model is revealed to be differentiated from three- and five-orbital models in their typical Hund metal active fillings. We identify distinctive regimes including four different correlated metals, one of which stems from the proximity to a Mott insulator, while the other three, which we call "intermediate" metal, weak Hund metal, and valence-skipping metal, from the effect of J being away from Mottness. Defining criteria characterizing these metals is suggested, establishing the existence of Hund metallicity in two-orbital systems.