Higher angular momentum pairing states in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi mathvariant="normal">Sr</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">RuO</mml:mi><mml:mn>4</mml:mn></mml:msub></mml:math> in the presence of longer-range interactions
Bibliographic record
Abstract
The superconducting symmetry of ${\mathrm{Sr}}_{2}\mathrm{Ru}{\mathrm{O}}_{4}$ remains a puzzle. Time-reversal symmetry breaking ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}+i{g}_{xy({x}^{2}\ensuremath{-}{y}^{2})}$ pairing has been proposed for reconciling multiple key experiments. However, its stability remains unclear. In this work, we theoretically study the superconducting instabilities in ${\mathrm{Sr}}_{2}\mathrm{Ru}{\mathrm{O}}_{4}$, including the effects of spin-orbit coupling (SOC), in the presence of both local and longer-range interactions within a random-phase approximation. We show that the inclusion of second-nearest-neighbor repulsions, together with nonlocal SOC in the ${B}_{2g}$ channel or orbital-anisotropy of the nonlocal interactions, can have a significant impact on the stability of both ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$- and $g$-wave pairing channels. We analyze the properties, such as Knight shift and spontaneous edge current, of the realized ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}+ig, {s}^{\ensuremath{'}}+i{d}_{xy}$, and mixed helical pairings in different parameter spaces, and we find that the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}+ig$ solution is in better agreement with the experimental data.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.002 | 0.001 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.013 | 0.001 |
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".