Complete phase diagram for three-band Hubbard model with orbital degeneracy lifted by crystal field splitting

TL;DR

This paper systematically maps the phase diagram of a three-band Hubbard model with lifted orbital degeneracy, revealing the conditions for orbital selective Mott phases influenced by Hund's coupling and crystal field splitting.

Contribution

It provides the first comprehensive phase diagram for this model using DMFT and Gutzwiller methods, highlighting the role of Hund's coupling and crystal field effects.

Findings

Orbital selective Mott phase stabilized by positive crystal field.

Hund's rule coupling is crucial for the orbital selective Mott phase.

High-spin to low-spin transition accompanies the Mott transition.

Abstract

Motivated by the unexplored complexity of the phase diagrams for multi-orbital Hubbard models, a three-band Hubbard model at integer fillings (N=4) with orbital degeneracy lifted partially by crystal field splitting is analyzed systematically in this work. By using single site dynamical mean-field theory and rotationally invariant Gutzwiller approximation, we have computed the full phase diagram with Coulomb interaction strength $U$ and crystal field splitting $\Delta$. We find a large region in the phase diagram, where an orbital selective Mott phase will be stabilized by the positive crystal field lifting the orbital degeneracy. Further analysis indicates that the Hund's rule coupling is essential for the orbital selective Mott phase and the transition toward this phase is accompanied by a high-spin to low-spin transition. Such a model may be relevant for the recently discovered pnictides and ruthenates correlated materials.