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

## TL;DR

This paper investigates the electronic behavior of three-band systems with crystal field splitting, revealing how Hund's coupling and interactions lead to orbital selective Mott transitions and Hund's metal phases, sensitive to crystal fields.

## Contribution

The study introduces a detailed analysis of Hund's metal regimes and orbital selective Mott transitions in three-band systems using a rotationally invariant slave boson approach, highlighting the effects of crystal field splitting.

## Key findings

- Orbital selective Mott transitions occur at critical U depending on electron filling.
- Hund's metal phase exists over a wide parameter range away from half-filling.
- Crystal fields strongly influence Hund's metal regimes and charge distribution.

## Abstract

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 $\Delta>0$ 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 $U_{c}(n)$. Away from the half-filled case $|n-3|\gtrsim 0.3$ there is a wide range of parameters for $U<U_c(n)$ 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.