Optical conductivity of tilted higher pseudospin Dirac-Weyl cones
Bibliographic record
Abstract
We investigate the finite-frequency optical response of systems described at low energies by Dirac-Weyl Hamiltonians with higher pseudospin $\mathcal{S}$ values. In particular, we examine the situation where a tilting term is applied in the Hamiltonian, which results in tilting of the Dirac electronic band structure. We calculate and discuss the optical conductivity for the cases $\mathcal{S}=1$, 3/2, and 2, in both two and three dimensions in order to demonstrate the expected signatures in the optical response. We examine both undertilted (type I) and overtilted (type II) as well as the critically tilted case (type III). Along with the well-known case of $\mathcal{S}=1/2$, a pattern emerges for any $\mathcal{S}$. We note that in situations with multiple nested cones, such as happens for $\mathcal{S}>1$, the possibility of having one cone being type I while the other is type II allows for more rich variations in the optical signature, which we will label as type-IV behavior. We also comment on the presence of optical sum rules in the presence of tilting. Finally, we discuss tilting in the $\ensuremath{\alpha}\ensuremath{-}{\mathrm{T}}_{3}$ model in two dimensions, which is a hybrid of the $\mathcal{S}=1/2$ (honeycomb lattice) and $\mathcal{S}=1$ (dice or ${\mathrm{T}}_{3}$ lattice) model with a variable Berry phase. We contrast this model's conductivity with that of $\mathcal{S}=3/2$ and $\mathcal{S}=2$ as the resultant optical response has some similarities, although there are clear distinguishing features between these cases.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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".