Third harmonic generation of undoped graphene in Hartree-Fock approximation
Bibliographic record
Abstract
We theoretically investigate the effects of Coulomb interaction, at the level of the unscreened Hartree-Fock approximation in an equation of motion framework, on third harmonic generation from undoped graphene. The unperturbed electronic states are described by a widely used two-band tight-binding model and the Coulomb interaction is described by the Ohno potential. The ground state is renormalized by taking into account the Hartree-Fock term and the optical conductivities are obtained by numerically solving the equations of motion. The absolute values of conductivity for third-harmonic generation depend on the photon frequency $\mathrm{\ensuremath{\Omega}}$ as ${\mathrm{\ensuremath{\Omega}}}^{\ensuremath{-}n}$ for $\ensuremath{\hbar}\mathrm{\ensuremath{\Omega}}<1$, and then show a peak as $3\ensuremath{\hbar}\mathrm{\ensuremath{\Omega}}$ approaches the renormalized energy of the $M$ point. Taking into account the Coulomb interaction, $n$ is found to be 5.5, which is significantly greater than the value of 4 found with the neglect of the Coulomb interaction. Therefore, the Coulomb interaction enhances third-harmonic generation at low photon energies---for our parameters $\ensuremath{\hbar}\mathrm{\ensuremath{\Omega}}<0.8$ eV---and then reduces it until the photon energy reaches about 2.1 eV. The effect of the background dielectric constant is also considered.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 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".