Optical properties of a semi-Dirac material
Bibliographic record
Abstract
Within a Kubo formalism we calculate the absorptive part of the dynamic longitudinal conductivity $\ensuremath{\sigma}(\mathrm{\ensuremath{\Omega}})$ of a two-dimensional (2D) semi-Dirac material. In the clean limit we provide separate analytic formulas for intraband (Drude) and interband contributions for $\ensuremath{\sigma}(\mathrm{\ensuremath{\Omega}})$ in both the relativistic and nonrelativistic directions. At finite doping, in the relativistic direction, a sum rule holds between the increase in optical spectral weight in the Drude component and that lost in the interband optical transitions. For the nonrelativistic direction, no such sum rule applies. Results are also presented when an energy gap opens in the energy dispersion. Numerical results due to finite residual scattering are provided and analytic results for the dc limit are derived. Energy dependence and possible anisotropy in the impurity scattering rate is considered. Throughout, we provide comparison of our results for $\sqrt{{\ensuremath{\sigma}}^{xx}{\ensuremath{\sigma}}^{yy}}$ with the corresponding results for graphene. A generalization of the 2D Hamiltonian to include powers of higher order than quadratic (nonrelativistic) and linear (relativistic) is considered. We also discuss the modifications introduced when an additional flat band is included via a semi-Dirac version of the $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathcal{T}}_{3}$ model, for which an $\ensuremath{\alpha}$ parameter tunes between the 2D semi-Dirac (graphenelike) limit and the semi-Dirac version of the dice or ${\mathcal{T}}_{3}$ lattice.
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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) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 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".