Orbital magnetization and anomalous Hall effect in interacting Weyl semimetals
Bibliographic record
Abstract
Ferromagnetic Weyl semimetals exhibit an anomalous Hall effect, a consequence of their topological properties. In the noninteracting case, the derivative of the orbital magnetization with respect to chemical potential is proportional to this anomalous Hall effect, the St\ifmmode \check{r}\else \v{r}\fi{}eda formula. Motivated by compounds such as ${\text{Mn}}_{3}\text{Sn}$, here we investigate how interactions modeled by a Hubbard $U$ impact on both quantities when the Fermi energy is either aligned with the Weyl nodes or away from them. Using dynamical mean-field theory, we first find interaction-induced Mott- and band-insulating transitions. In the Weyl semimetal regime, away from insulators, interactions lead to an increase in the imbalance between the densities of spin species induced by a Zeeman term $h$. This increased imbalance leads to an increase of the anomalous Hall effect that can also be understood from the displacement of the Weyl nodes and topological arguments. This interaction-induced spin imbalance also compensates the reduction in orbital magnetization of each spin species that comes from smaller quasiparticle weight. In the small interaction regime, the combined effects lead to an orbital magnetization that depends weakly on interaction and still changes linearly with chemical potential at small doping. In the intermediate and strong correlation regimes, the localization due to interaction affects strongly the orbital magnetization, which becomes small. A quasiparticle picture explains the anomalous Hall effect but does not suffice for the orbital magnetization. We propose a modified St\ifmmode \check{r}\else \v{r}\fi{}eda formula to relate anomalous Hall effect and orbital magnetization in the weak correlation limit. We also identify mirror and particle-hole symmetries of the lattice model that explain, respectively, the vanishing of the anomalous Hall effect at $h=0$ for all $U$ and $\ensuremath{\mu}$ of the orbital magnetization at half-filling $\ensuremath{\mu}=0$ for all $U$ and $h$.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.002 | 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 | 0.001 |
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".