Integral quantum Hall effect in graphene: Zero and finite Hall field
Bibliographic record
Abstract
We study the influence of a finite Hall field ${E}_{H}$ on the Hall conductivity ${\ensuremath{\sigma}}_{\mathit{yx}}$ in graphene. Analytical expressions are derived for ${\ensuremath{\sigma}}_{\mathit{yx}}$ using the Kubo-Greenwood formula. For vanishing ${E}_{H}$, we obtain the well-known expression ${\ensuremath{\sigma}}_{\mathit{yx}}=4(N+1/2){e}^{2}/h$. The inclusion of the dispersion of the energy levels, previously not considered, and their width, due to scattering by impurities, produces the plateau of the $n=0$ Landau level. Further, we evaluate the longitudinal resistivity ${\ensuremath{\rho}}_{\mathit{xx}}$ and show that it exhibits an oscillatory behavior with the electron concentration. The peak values of ${\ensuremath{\rho}}_{\mathit{xx}}$ depend strongly on the impurity concentration and their potential. For a finite ${E}_{H}$, the result for ${\ensuremath{\sigma}}_{\mathit{yx}}$ is the same as that for ${E}_{H}=0$, provided ${E}_{H}$ is not strong, but the values and positions of the resistivity maxima are modified due to the ${E}_{H}$-dependent dispersion of the energy levels.
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How this classification was reachedexpand
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 | 0.000 | 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 | 0.000 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".