Charge Disproportionation without Charge Transfer in the Rare-Earth-Element Nickelates as a Possible Mechanism for the Metal-Insulator Transition
Bibliographic record
Abstract
We study a model for the metal-insulator ($M\text{\ensuremath{-}}I$) transition in the rare-earth-element nickelates $R{\mathrm{NiO}}_{3}$, based upon a negative charge transfer energy and coupling to a rocksaltlike lattice distortion of the ${\mathrm{NiO}}_{6}$ octahedra. Using exact diagonalization and the Hartree-Fock approximation we demonstrate that electrons couple strongly to these distortions. For small distortions the system is metallic, with a ground state of predominantly ${d}^{8}L$ character, where $\underset{_}{L}$ denotes a ligand hole. For sufficiently large distortions ($\ensuremath{\delta}{d}_{\mathrm{Ni}\text{\ensuremath{-}}\mathrm{O}}\ensuremath{\sim}0.05--0.10\text{ }\text{ }\AA{}$), however, a gap opens at the Fermi energy as the system enters a periodically distorted state alternating along the three crystallographic axes, with $({d}^{8}{\underset{_}{L}}^{2}{)}_{S=0}({d}^{8}{)}_{S=1}$ character, where $S$ is the total spin. Thus the $M\text{\ensuremath{-}}I$ transition may be viewed as being driven by an internal volume ``collapse'' where the ${\mathrm{NiO}}_{6}$ octahedra with two ligand holes shrink around their central Ni, while the remaining octahedra expand accordingly, resulting in the ($1/2$, $1/2$, $1/2$) superstructure observed in x-ray diffraction in the insulating phase. This insulating state is an example of charge ordering achieved without any actual movement of the charge.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".