Twist angle dependence of flatbands in trilayer graphene: A first-principles study
Bibliographic record
Abstract
Among the most classical two-dimensional (2D) heterostructures, graphene stands out to exhibit unique electronic properties through manipulations of stacking layers, twist angles, strain, and external electric and magnetic fields. In this work, we present a theoretical investigation of twisted trilayer graphene (tTLG) using first-principles calculations, considering various twist angles θ12, which is the angle between the bottom and middle layers, and θ23, which is the angle between the top and middle layers. For trilayer configurations AÃA, where θ23 = θ12, and AÃÃ′, where θ23≠θ12, supercells as large as containing 23 338 atoms are built to capture the impact of twist angles on the electronic properties in tTLG using RESCU+. We discover that flatbands (with bandwidths less than 100 meV) can emerge when the twist angles approach certain magic angles while θ12⋅θ23 > 0. The bandwidth minimizes near these magic angles and varies smoothly with the twist angle, exhibiting no abrupt changes. Despite the symmetry being affected by the shift of the bottom and top layers leading to the changes in the Dirac cones, the flatbands exhibit remarkable robustness and retain their distinct properties. Our findings explain why the correlated states can also exist at twist angles slightly away from the exact magic angles.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".