Surface theory of a second-order topological insulator beyond the Dirac approximation
Bibliographic record
Abstract
We study the surface states and chiral hinge states of a three-dimensional second-order topological insulator in the presence of an external magnetic gauge field. Surfaces pierced by flux host Landau levels, while surfaces parallel to the applied field are not significantly affected. The chiral hinge modes mediate spectral flow between neighboring surfaces. As the magnetic field strength is increased, the surface Landau quantization deviates from that of a massive Dirac cone. Quantitatively, the $n=0$ Landau level falls inside the surface Dirac gap and not at the gap edge. The $n\ensuremath{\ne}0$ levels exhibit a further, qualitative discrepancy: while the massive Dirac cone is expected to produce pairs of levels ($\ifmmode\pm\else\textpm\fi{}n$) which are symmetric around zero energy, the $n$ and $\ensuremath{-}n$ levels become asymmetric in our lattice model---one of the pair may even be absent from the spectrum or hybridized with the continuum. In order to resolve the issue, we extend the standard two-dimensional (2D) massive Dirac surface theory by including additional Hamiltonian terms at $O({\mathbf{k}}^{2})$. While these terms do not break particle-hole symmetry in the absence of magnetic field, they lead to the aforementioned Landau level asymmetry once the magnetic field is applied. We argue that similar $O({\mathbf{k}}^{2})$ correction terms are generically expected in lattice models containing gapped Dirac fermions, using the BHZ model of a 2D topological insulator as an example.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".