Theory of spin response in underdoped cuprates as strongly fluctuating<i>d</i>-wave superconductors
Bibliographic record
Abstract
We study the spin dynamics in underdoped cuprates at low temperatures by considering them as quasi-two-dimensional d-wave superconductors with strong quantum phase fluctuations. An effective theory of spin degrees of freedom of nodal quasiparticles coupled to vortex defects in the phase of the superconducting order parameter is formulated. It represents the minimal extension of the three-dimensional QED theory of the pseudogap phase into the superconducting region. The theory predicts a single superconductor-spin-density wave (SC-SDW) phase transition, without coexistence between the two phases. At the transition, which may be fluctuation-induced first order, vortices condense (and SC is lost) and the chiral symmetry for fermions simultaneously breaks (and SDW is formed). We compute the spin-spin correlation function in the fluctuating superconducting state and explain the evolution of the spin response with energy in underdoped ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6+x}$ observed in neutron-scattering experiments. In particular, we predict that at very low frequencies $\ensuremath{\omega}\ensuremath{\sim}(1/10){\ensuremath{\omega}}_{\mathrm{res}},$ with ${\ensuremath{\omega}}_{\mathrm{res}}$ being the energy of the ``resonance'' at $\stackrel{\ensuremath{\rightarrow}}{Q}=(\ensuremath{\pi},\ensuremath{\pi}),$ (weak) spin response should become narrowly peaked at four diagonally incommensurate wave vectors that span between the nodes of the superconducting order parameter. These peaks represent the inherent collective mode of the phase fluctuating d-wave superconductor, the condensation of which would bring about the SDW order in the pseudogap phase. Our interpretation of the resonance suggests that it should become more elusive in the superconductors with lower ${T}_{c},$ in accord with its conspicuous absence in ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{4}.$
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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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| 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".