Linear response of a Chern insulator to finite-frequency electric fields
Bibliographic record
Abstract
We derive the macroscopic charge and current densities of a Chern insulator initially occupying its electronic ground state as it responds to a finite-frequency electric field; we use a previously developed formalism based on microscopic polarization and magnetization fields in extended media. In a topologically trivial insulator, our result reduces to the familiar expression for the induced current density in linear response obtained from a Kubo analysis. But for a Chern insulator we find an extra "topological" term involving the (first) Chern number associated with the occupied bands, encoding the quantum anomalous Hall effect in the presence of a frequency-dependent electric field. While an analogous term has been introduced in the "modern theories of polarization and magnetization" for the linear response of finite-sized systems to static electric fields, our expression is valid for bulk Chern insulators in the presence of both static and finite-frequency electric fields, being derived analytically from a microscopic treatment of the electronic degrees of freedom, and can be generalized in a straightforward way to describe the response of a Chern insulator to electromagnetic fields that are not only frequency-dependent but also spatially inhomogeneous.
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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 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 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".