Particle-hole asymmetry on Hall conductivity of a topological insulator
Bibliographic record
Abstract
The helical Dirac states on the surface of a topological insulator are protected by topology and display significant particle-hole asymmetry. This asymmetry arises from a subdominant Schr\"odinger-type contribution to the Hamiltonian which provides a small perturbation to a dominant Dirac contribution. This changes the Landau level energies in an external magnetic field ($B$) and provides modifications to the usual relativistic optical matrix elements. Nevertheless we find that the relativistic quantization of the Hall plateaus remains even when the ratio of the Schr\"odinger (${E}_{0}$) to Dirac (${E}_{1}$) magnetic energy scale increases either through an increase in $B$, a decrease in the Schr\"odinger mass, or a decrease of the Dirac Fermi velocity. First corrections to the optical matrix elements (OMEs) in the relativistic case drop out at least to order ${({E}_{0}/{E}_{1})}^{3}$. In the opposite limit ${E}_{1}$ small, the quantization remains classical but there is a split into two series. The first corrections to the OMEs in this case cancel out at least to order ${({E}_{1}/{E}_{0})}^{4}$.
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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) | 0.001 | 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) | 0.001 | 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 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".