Anomalous behavior in the magneto-optics of a gapped topological insulator
Bibliographic record
Abstract
The Dirac fermions at the surface of a topological insulator can be gapped by introducing magnetic dopants. Alternatively, in an ultrathin slab with thickness on the order of the extent of the surface states, both the top and bottom surface states acquire a common gap value $(\mathrm{\ensuremath{\Delta}})$ but with opposite sign. In a topological insulator, the dominant piece of the Hamiltonian $(\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{H})$ is of a relativistic nature. A subdominant nonrelativistic piece is also present and, in an external magnetic field $(B)$ applied perpendicular to the surface, the $N=0$ Landau level is no longer at zero energy but is shifted to positive energy by the Schr\"odinger magnetic energy. When a gap is present, it further shifts this level down by $\ensuremath{-}\mathrm{\ensuremath{\Delta}}$ for positive $\mathrm{\ensuremath{\Delta}}$ and up by $|\mathrm{\ensuremath{\Delta}}|$ for a negative gap. This has important consequences for the magneto-optical properties of such systems. In particular, at charge neutrality, the lowest energy transition displays anomalous nonmonotonic behavior as a function of $B$ in both its position in energy and its optical spectral weight. The gap can also have a profound impact on the spectral weight of the interband lines and on corresponding structures in the real part of the dynamical Hall conductivity. Conversely, the interband background in zero field remains unchanged by the nonrelativistic term in $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{H}$ (although its onset frequency is modified).
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 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".