Integer quantum Hall effect in gapped single-layer graphene
Bibliographic record
Abstract
Analytical expressions for the Hall conductivity ${\ensuremath{\sigma}}_{yx}$ and the longitudinal resistivity ${\ensuremath{\rho}}_{xx}$ are derived in gapped, single-layer graphene using linear response theory. The gap $2\ensuremath{\Delta}$, described by a mass term, is induced by a substrate made of hexagonal boron nitride (h-BN) and produces two levels at $\ifmmode\pm\else\textpm\fi{}\ensuremath{\Delta}$. It is shown that ${\ensuremath{\sigma}}_{yx}$ has the same form as for a graphene sample supported by a common substrate without a mass term. The differences are a shift in the energy spectrum, which is not symmetric with respect to the Dirac point for either valley due to the gap, the absence of a zero-energy Landau level, and the nonequivalence of the $K$ and ${K}^{\ensuremath{'}}$ valleys. In addition, the dis-persion of the energy levels, caused by electron scattering by impurities, modifies mostly plateaus due to the levels at $\ifmmode\pm\else\textpm\fi{}\ensuremath{\Delta}$. It is shown that the resistivity ${\ensuremath{\rho}}_{xx}$ exhibits an oscillatory dependence on the electron concentration. The main difference with the usual graphene samples, on SiO${}_{2}$ substrates, occurs near zero concentration, as the energy spectra differ mostly near the Dirac point.
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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 | 0.001 | 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 | 0.002 |
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".