Coulomb interaction and magnetic catalysis in the quantum Hall effect in graphene
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Bibliographic record
Abstract
The dynamics of symmetry breaking responsible for lifting the degeneracy of the Landau levels in the integer quantum Hall effect in graphene is studied in a low-energy model with the Coulomb interaction. The gap equation for Dirac quasiparticles is analyzed for both the lowest and higher Landau levels, taking into account the Landau levels mixing. It is shown that the characteristic feature of the long-range Coulomb interaction is the decrease of the gap parameters with increasing the Landau level index $n$ ("running" gaps). The renormalization (running) of the Fermi velocity as a function of $n$ is also studied. The solutions of the gap equation reproduce correctly the experimentally observed integer quantum Hall plateaus in graphene in strong magnetic fields.
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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 | 0.001 | 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 it