Highly anisotropic optical conductivities in two-dimensional tilted semi-Dirac bands
Bibliographic record
Abstract
Within linear response theory, the absorptive part of highly anisotropic optical conductivities are analytically calculated for distinct tilts in two-dimensional (2D) tilted semi-Dirac bands (SDBs). The transverse optical conductivities always vanish. The interband longitudinal optical conductivities (LOCs) in 2D tilted SDBs differ qualitatively in the power-law scaling of $\ensuremath{\omega}$ as $\mathrm{Re}{\ensuremath{\sigma}}_{\ensuremath{\perp}}^{\mathrm{IB}}(\ensuremath{\omega})\ensuremath{\propto}{\ensuremath{\sigma}}_{0}\sqrt{\ensuremath{\omega}}$ and $\mathrm{Re}{\ensuremath{\sigma}}_{\ensuremath{\parallel}}^{\mathrm{IB}}(\ensuremath{\omega})\ensuremath{\propto}{\ensuremath{\sigma}}_{0}/\sqrt{\ensuremath{\omega}}$. By contrast, the intraband LOCs in 2D tilted SDBs depend on $\ensuremath{\mu}$ in the power-law scaling as $\mathrm{Re}{\ensuremath{\sigma}}_{\ensuremath{\perp}}^{\mathrm{D}}(\ensuremath{\omega})\ensuremath{\propto}{\ensuremath{\sigma}}_{0}\ensuremath{\mu}\sqrt{\ensuremath{\mu}}$ and $\mathrm{Re}{\ensuremath{\sigma}}_{\ensuremath{\parallel}}^{\mathrm{D}}(\ensuremath{\omega})\ensuremath{\propto}{\ensuremath{\sigma}}_{0}\ensuremath{\mu}/\sqrt{\ensuremath{\mu}}$. The tilt-dependent behaviors of LOCs could qualitatively characterize distinct impact of band tilting in 2D tilted SDBs. In particular, for arbitrary tilt $t$ satisfying $0<t\ensuremath{\le}2$, the interband LOCs always possess a robust fixed point at $\ensuremath{\omega}=2\ensuremath{\mu}$. The power-law scalings and tilt-dependent behaviors further dictate significant differences in the asymptotic background values and angular dependence of LOCs. Our theoretical predictions should be valid for a broad class of 2D tilted SDB materials, and can also be used to fingerprint 2D tilted SDB from 2D untilted SDB as well as tilted Dirac bands.
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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) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.003 |
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; both teacher heads agree on what is shown here.
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".