Kronig-Penney model on bilayer graphene: Spectrum and transmission periodic in the strength of the barriers
Bibliographic record
Abstract
We show that the transmission through single and double $\ensuremath{\delta}$-function potential barriers of strength $P=V{W}_{b}/\ensuremath{\hbar}{v}_{F}$ in bilayer graphene is periodic in $P$ with period $\ensuremath{\pi}$. For a certain range of $P$ values we find states that are bound to the potential barrier and that run along the potential barrier. Similar periodic behavior is found for the conductance. The spectrum of a periodic succession of $\ensuremath{\delta}$-function barriers (Kronig-Penney model) in bilayer graphene is periodic in $P$ with period $2\ensuremath{\pi}$. For $P$ smaller than a critical value ${P}_{c}$, the spectrum exhibits two Dirac points while for $P$ larger than ${P}_{c}$ an energy gap opens. These results are extended to the case of a superlattice of $\ensuremath{\delta}$-function barriers with $P$ alternating in sign between successive barriers; the corresponding spectrum is periodic in P with period $\ensuremath{\pi}$.
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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".