Conservation laws, vertex corrections, and screening in Raman spectroscopy
Bibliographic record
Abstract
We present a microscopic theory for the Raman response of a clean multiband superconductor, with emphasis on the effects of vertex corrections and long-range Coulomb interaction. The measured Raman intensity, $R(\mathrm{\ensuremath{\Omega}})$, is proportional to the imaginary part of the fully renormalized particle-hole correlator with Raman form factors $\ensuremath{\gamma}(\stackrel{P\vec}{k})$. In a BCS superconductor, a bare Raman bubble is nonzero for any $\ensuremath{\gamma}(\stackrel{P\vec}{k})$ and diverges at $\mathrm{\ensuremath{\Omega}}=2{\mathrm{\ensuremath{\Delta}}}_{\mathrm{max}}$, where ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{max}}$ is the largest gap along the Fermi surface. However, for $\ensuremath{\gamma}(\stackrel{P\vec}{k})$ = constant, the full $R(\mathrm{\ensuremath{\Omega}})$ is expected to vanish due to particle number conservation. It was sometimes stated that this vanishing is due to the singular screening by long-range Coulomb interaction. In our general approach, we show diagrammatically that this vanishing actually holds due to vertex corrections from the same short-range interaction that gives rise to superconductivity. We further argue that long-range Coulomb interaction does not affect the Raman signal for any $\ensuremath{\gamma}(\stackrel{P\vec}{k})$. We argue that vertex corrections eliminate the divergence at $2{\mathrm{\ensuremath{\Delta}}}_{\mathrm{max}}$. We also argue that vertex corrections give rise to sharp peaks in $R(\mathrm{\ensuremath{\Omega}})$ at $\mathrm{\ensuremath{\Omega}}<2{\mathrm{\ensuremath{\Delta}}}_{\mathrm{min}}$ (the minimum gap along the Fermi surface), when $\mathrm{\ensuremath{\Omega}}$ coincides with the frequency of one of the collective modes in a superconductor, e.g., Leggett and Bardasis-Schrieffer modes in the particle-particle channel, and an excitonic mode in the particle-hole channel.
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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) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| 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".