Dirac electrons in Moiré superlattice: From two to three dimensions
Bibliographic record
Abstract
Moir\'e patterns in van der Waals (vdW) heterostructures bring novel physical effects to the materials. We report theoretical investigations of the Moir\'e pattern formed by graphene (Gr) on hexagonal boron nitride $(h\text{BN})$. For both the two-dimensional (2D) flat-sheet and the freestanding three-dimensional (3D) wavelike film geometries, the behaviors of Dirac electrons are strongly modulated by the local high-symmetry stacking configurations of the Moir\'e pattern. In the 2D flat sheet, the secondary Dirac cone (SDC) dispersion emerges due to the stacking-selected localization of SDC wave functions, while the original Dirac cone (ODC) gap is suppressed due to an overall effect of ODC wave functions. In the freestanding 3D wavelike Moir\'e structure, we predict that a specific local stacking in the Moir\'e superlattice is promoted at the expense of other local stackings, leading to an electronic structure more similar to that of the perfectly matching flat Gr/$h\text{BN}$ than that of the flat-sheet 2D Moir\'e pattern. To capture the overall picture of the Moir\'e superlattice, supercells containing 12 322 atoms are simulated by first principles.
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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) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.000 |
| 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".