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 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 | 0.002 |
| 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 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 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 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".