Electronic properties of disordered corner-sharing tetrahedral lattices
Bibliographic record
Abstract
We have examined the behavior of noninteracting electrons moving on a corner-sharing tetrahedral lattice into which we introduce a uniform (box) distribution, of width $W$, of random on-site energies. We have used both the relative localization length and the spectral rigidity to analyze the nature of the eigenstates and have determined both the mobility-edge trajectories as a function of $W$ and the critical disorder ${W}_{c}$, beyond which all states are localized. We find (i) that the mobility-edge trajectories (energies ${E}_{c}$ versus disorder $W$) are qualitatively different from those found for a simple cubic lattice and (ii) that the spectral rigidity is scale invariant at ${W}_{c}$ and thus provides a reliable method of estimating this quantity---we find ${W}_{c}∕t=14.5$. We then discuss our results in the context of the metal-to-insulator transition undergone by $\mathrm{Li}{\mathrm{Al}}_{y}{\mathrm{Ti}}_{2\ensuremath{-}y}{\mathrm{O}}_{4}$ in a quantum-site percolation model that also includes the above-mentioned Anderson disorder. We show that the effects of an inhomogeneous distribution of on-site energies produced by the Al impurity potentials are small compared to those produced by quantum-site percolation, at least in the determination of the doping concentration at which the metal-to-insulator transition is predicted to occur.
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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 | 0.000 | 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 | 0.000 | 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) | 0.000 | 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".