Quantum anomalous Hall effect on a square lattice with spin–orbit couplings and an exchange field
Bibliographic record
Abstract
We investigate a tight-binding model on a two-dimensional square lattice with three terms: the Rashba spin–orbit coupling, the real amplitude next-nearest spin–orbit coupling, and an exchange field. We calculate the first Chern number to identify band topology. It is found that the Chern number takes the quantized values of C 1 = 1, 2 and the chiral edge modes can be obtained. Therefore our model realizes the quantum anomalous Hall (QAH) effect. The Rashba coupling is positive for the QAH phase while the next-nearest coupling is detrimental to it. By increasing the exchange field intensity, the Chern number changes from quantized value 2 to 0. The behavior of the edge states is also studied. Particularly for C 1 = 2 case, there are two gapless spin-polarized edge states with the same spin polarization moving in the same spatial direction. This indicates that their appearance is topological rather than accidental.
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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) | 0.000 | 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) | 0.001 | 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".