Ultrasound attenuation in the unconventional superconductor SR(2)RUO(4)
Bibliographic record
Abstract
Sr2RuO4 is an unconventional superconductor with a critical temperature of 1.5 K. It is highly two-dimensional and of a similar crystal structure as the high-Tc cuprates. In contrast to the cuprates it is believed to be a triplet superconductor. The generic symmetry of the order parameter is p-wave with a full gap in all directions. However recent measurements of heat capacity, penetration depth, thermal conductivity and NMR lattice relaxation time have shown power-law temperature dependences indicative of nodes in the gap. In order to locate the position of these nodes, we performed ultrasound attenuation measurements. At low temperature, changes in the ultrasound attenuation are electronic in origin. When performed at low frequency, in the hydrodynamic limit, the electronic attenuation is proportional to the electron viscosity which is a tensor of rank four. Hence there are six independent elements of which three describe all the in-plane sound modes. A difference in the temperature dependence between these modes can reveal the position of nodes in some cases. We measured the attenuation of four in-plane modes and one out-of-plane mode. Together they describe four of the viscosity components. Our first observation is that the normal state in-plane viscosity is highly anisotropic. Transverse waves polarized in the plane are a thousand times less attenuating when they propagate along the [100] direction than along [110]. In the superconducting state, the T dependence of the attenuation follows a power-law down to 40 mK, or Tc/30. This confirms the presence of nodes in the gap. We also observed some anisotropy in the amplitude and exponent of the low temperature power-laws. This anisotropy is weak suggesting horizontal line nodes instead of vertical line nodes. The best fit to the entire data was obtained with the model of Zhitomirsky and Rice in which horizontal line nodes are present only on two of the three Fermi surfaces, the third one being fully gapped. If this agreement is confirmed by careful calculations, then it would represent compelling evidence for the identification of the gap symmetry.
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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 | 0.000 | 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) | 0.001 | 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".