Universal relationship between the energy scales of the pseudogap phase, the superconducting state, and the charge-density-wave order in copper oxide superconductors
Bibliographic record
Abstract
We report the hole doping dependencies of the pseudogap phase energy scale $2{\mathrm{\ensuremath{\Delta}}}_{\mathrm{PG}}$, the antinodal (nodal) superconducting energy scales $2{\mathrm{\ensuremath{\Delta}}}_{\mathrm{SC}}^{\text{AN}}$ ($2{\mathrm{\ensuremath{\Delta}}}_{\mathrm{SC}}^{\text{N}}$), and the charge-density-wave energy scale $2{\mathrm{\ensuremath{\Delta}}}_{\mathrm{CDW}}$ extracted from the electronic Raman responses of several copper oxide families. We show for all the cuprates studied that the three energy scales $2{\mathrm{\ensuremath{\Delta}}}_{\mathrm{PG}}, 2{\mathrm{\ensuremath{\Delta}}}_{\mathrm{SC}}^{\text{AN}}$, and $2{\mathrm{\ensuremath{\Delta}}}_{\mathrm{CDW}}$ display the same decreasing monotonic behavior with doping. In particular, $2{\mathrm{\ensuremath{\Delta}}}_{\mathrm{SC}}^{\text{AN}}$ and $2{\mathrm{\ensuremath{\Delta}}}_{\mathrm{CDW}}$ have nearly equal values. This suggests a universal scenario in which $2{\mathrm{\ensuremath{\Delta}}}_{\mathrm{PG}}, 2{\mathrm{\ensuremath{\Delta}}}_{\mathrm{SC}}^{\text{AN}}$, and $2{\mathrm{\ensuremath{\Delta}}}_{\mathrm{CDW}}$ are governed by common microscopic interactions that become relevant well above the superconducting transition at ${T}_{c}$. This is to be contrasted with the behavior of the nodal superconducting energy scale $2{\mathrm{\ensuremath{\Delta}}}_{\mathrm{SC}}^{\text{N}}$, which tracks the doping dependence of ${T}_{c}$ and, hence, seems to be controlled by different interactions.
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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 | 0.001 |
| 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 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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".