Hund's metal regimes and orbital selective Mott transitions in three band systems

We analyze the electronic properties of interacting crystal field split three band systems. Using a rotationally invariant slave boson approach we analyze the behavior of the electronic mass renormalization as a function of the intralevel repulsion U, the Hund's coupling J, the crystal field splitting, and the number of electrons per site n. We first focus on the case in which two of the bands are identical and the levels of the third one are shifted by [Formula: see text] with respect to the former. We find an increasing quasiparticle mass differentiation between the bands, for system away from half-filling (n  =  3), as the Hubbard interaction U is increased. This leads to orbital selective Mott transitions where either the higher energy band (for 4  >  n  >  3) or the lower energy degenerate bands (2  <  n  <  3) become insulating for U larger than a critical interaction [Formula: see text]. Away from the half-filled case [Formula: see text] there is a wide range of parameters for [Formula: see text] where the system presents a Hund's metal phase with the physics dominated by the local high spin multiplets. Finally, we study the fate of the n  =  2 Hund's metal as the energy splitting between orbitals is increased for different possible crystal distortions. We find a strong sensitivity of the Hund's metal regime to crystal fields due to the opposing effects of J and the crystal field splittings on the charge distribution between the bands.