Valence-skipping and negative-U in the d-band from repulsive local Coulomb interaction

TL;DR

This paper demonstrates that local Coulomb interactions can cause valence-skipping in the d-band, leading to negative-U effects, especially in specific d-electron fillings, and explains their connection to superconductivity.

Contribution

It reveals that anisotropic orbital-multipole scattering from Coulomb interactions induces valence-skipping, providing explicit phase boundaries and contrasting valence distributions with Hund's metals.

Findings

Valence-skipping occurs in d^1, d^4, d^6, d^9 fillings.

Explicit phase boundaries for valence-skipping are derived.

Valence-skipping metals differ from Hund's metals in local valence distribution.

Abstract

We show that repulsive local Coulomb interaction alone can drive valence-skipping charge disproportionation in the degenerate d-band, resulting in effective negative-U. This effect is shown to originate from anisotropic orbital-multipole scattering, and occurs only for $d^1$, $d^4$, $d^6$ and $d^9$ fillings (and their immediate surroundings). Explicit boundaries for valence-skipping are derived and the paramagnetic phase diagram for $d^4$ and $d^6$ is calculated. We also establish that the valence-skipping metal is very different, in terms of its local valence distribution, compared to the atomic-like Hund's metal. These findings explains why transition metal compounds with the aforementioned d-band fillings are more prone to valence-skipping charge order and anomalous superconductivity.