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 distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 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 | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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 teacher head, 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".