Hybrid Wannier Chern bands in magic angle twisted bilayer graphene and the quantized anomalous Hall effect
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Bibliographic record
Abstract
We propose a method for studying the strong interaction regimes in twisted bilayer graphene using hybrid Wannier functions that are Wannier-like in one direction and Bloch-like in the other. We focus on the active bands as given by the continuum model proposed by Bistritzer and MacDonald, [Proc. Natl. Acad. Sci. 108, 12233 (2011)] and discuss the properties of corresponding hybrid Wannier functions. We then employ the method for a study of the fillings of 3 electrons per moir cell using the Hartree-Fock method. We discuss at length different regimes under which a quantized anomalous Hall effect is seen in these two fillings.
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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 | 0.004 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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 it