Magic angle butterfly in twisted trilayer graphene
Why this work is in the frame
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Bibliographic record
Abstract
We consider a configuration of three stacked graphene monolayers with commensurate twist angles ${\ensuremath{\theta}}_{12}/{\ensuremath{\theta}}_{23}=p/q$, where $p$ and $q$ are coprime integers with $0<p<|q|$ and $q$ can be positive or negative. We study this system using the continuum model in the chiral limit when interlayer coupling terms between ${\text{AA}}_{12}$ and ${\text{AA}}_{23}$ sites of the moir\'e patterns 12 and 23 are neglected. There are only three inequivalent displacements between the moir\'e patterns 12 and 23, at which the three monolayers' Dirac zero modes are protected. Remarkably, for these displacements and an arbitrary $p/q$ we discover exactly flat bands at an infinite set of twist angles (magic angles). We provide theoretical explanation and classification of all possible configurations and topologies of the flat bands.
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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 | 0.003 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.005 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.012 |
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 it