Bibliographic record
Abstract
We present a new general formalism for investigating the second-order optical response of solids, and illustrate it by deriving expressions for the second-order susceptibility tensor ${\ensuremath{\chi}}_{2}(\ensuremath{-}{\ensuremath{\omega}}_{\ensuremath{\Sigma}};{\ensuremath{\omega}}_{\ensuremath{\beta}},{\ensuremath{\omega}}_{\ensuremath{\gamma}}),$ where ${\ensuremath{\omega}}_{\ensuremath{\Sigma}}={\ensuremath{\omega}}_{\ensuremath{\beta}}+{\ensuremath{\omega}}_{\ensuremath{\gamma}},$ for clean, cold semiconductors in the independent particle approximation. Based on the identification of a polarization operator $\mathbf{P}$ that would be valid even in a more complicated many-body treatment, the approach avoids apparent, unphysical divergences of the nonlinear optical response at zero frequency that sometimes plague such calculations. As a result, it allows for a careful examination of $\mathit{actual}$ divergences associated with physical phenomena that have been studied before, but not in the context of nonlinear optics. These are (i) a coherent current control effect called ``injection current,'' or ``circular photocurrent,'' and (ii) photocurrent due to the shift of the center of electron charge in noncentrosymmetric materials in the process of optical excitation, called ``shift current.'' The expressions we present are amenable for numerical calculations, and we demonstrate this by performing a full band-structure calculation of the shift current coefficient for GaAs.
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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 | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".