Unified theory of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>ab</mml:mi></mml:math>-plane and<i>c</i>-axis penetration depths of underdoped cuprates
Bibliographic record
Abstract
We formulate a model describing the doping (x) and temperature (T) dependence of the $\mathrm{ab}\ensuremath{-}\mathrm{p}\mathrm{l}\mathrm{a}\mathrm{n}\mathrm{e}$ and c-axis penetration depth of a cuprate superconductor. The model incorporates the suppression of the superfluid density with underdoping as the system approaches the Mott-Hubbard insulating state by augmenting a d-wave BCS model with a phenomenological charge renormalization factor that is vanishingly small for states away from the nodes of the d-wave pair potential but close to unity in the vicinity of the nodes. The c-axis penetration depth is captured within a model of incoherent electron tunneling between the ${\mathrm{CuO}}_{2}$ planes. Application of this model to the recent experimental data on the high-purity single crystals of ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6+\ensuremath{\delta}}$ implies existence of a ``nodal protectorate,'' a k-space region in the vicinity of the nodes whose size decreases in proportion to x, in which d-wave quasiparticles remain sharp even as the system teeters on the brink of becoming an insulator. The superfluid density, which is extremely small for these samples, also appears to come exclusively from these protected nodal regions.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 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) | 0.000 | 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 teacher head, 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".