Enhancement of charge instabilities in Hund's metals by the breaking of rotational symmetry

TL;DR

This paper investigates how breaking rotational symmetry in Hund's metals enhances charge instabilities, leading to divergent electronic compressibility, especially relevant for materials like iron-based superconductors.

Contribution

It demonstrates that spin-anisotropy and crystal-field splitting extend the charge instability region in Hund's metals, linking it to local degree of freedom freezing.

Findings

Breaking rotational invariance promotes charge instability.

Charge instability region expands with spin-anisotropy and crystal-field splitting.

Instability is connected to rapid changes in electronic kinetic energy.

Abstract

We analyze multi-orbital Hubbard models describing Hund's metals, focusing on the ubiquitous occurrence of a charge instability, signalled by a divergent/negative electronic compressibility, in a range of doping from the half-filled Mott insulator corresponding to the frontier between Hund's and normal metals. We show that the breaking of rotational invariance favors this instability: both spin-anisotropy in the interaction and crystal-field splitting among the orbitals make the instability zone extend to larger dopings, making it relevant for real materials like iron-based superconductors. These observations help us build a coherent picture of the occurrence and extent of this instability. We trace it back to the partial freezing of the local degrees of freedom in the Hund's metal, which reduces the allowed local configurations and thus the quasiparticle itinerancy. The abruptness of the unfreezing happening at the Hund's metal frontier can be directly connected to a rapid change in the electronic kinetic energy and thus to the enhancement and divergence of the compressibility.