Low-energy description of the metal-insulator transition in the rare-earth nickelates

TL;DR

This paper presents a minimal theoretical model explaining the metal-insulator transition in rare-earth nickelates through bond-disproportionation driven by electron interactions, emphasizing the roles of Hund's coupling and charge-transfer energy.

Contribution

It introduces a simple two-orbital model capturing the transition, highlighting the importance of Hund's coupling and bond-disproportionation in the insulating state.

Findings

Bond-disproportionation induces a paramagnetic insulator over a wide parameter range.

Large Hund's coupling promotes spontaneous bond-disproportionation.

Small or negative charge-transfer energy is crucial for the transition.

Abstract

We propose a simple theoretical description of the metal-insulator transition of rare-earth nickelates. The theory involves only two orbitals per nickel site, corresponding to the low-energy anti-bonding $e_g$ states. In the monoclinic insulating state, bond-length disproportionation splits the manifold of $e_g$ bands, corresponding to a modulation of the effective on-site energy. We show that, when subject to a local Coulomb repulsion $U$ and Hund's coupling $J$, the resulting bond-disproportionated state is a paramagnetic insulator for a wide range of interaction parameters. Furthermore, we find that when $U-3J$ is small or negative, a spontaneous instability to bond disproportionation takes place for large enough $J$. This minimal theory emphasizes that a small or negative charge-transfer energy, a large Hund's coupling, and a strong coupling to bond-disproportionation are the key factors underlying the transition. Experimental consequences of this theoretical picture are discussed.