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.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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".