Classification of Lifshitz invariant in multiband superconductors: An application to Leggett modes in the linear response regime in Kagome lattice models
Bibliographic record
Abstract
Multiband superconductors are sources of rich physics arising from multiple order parameters, which show unique collective dynamics including Leggett mode as relative phase oscillations. Previously, it has been pointed out that the Leggett mode can be optically excited in the linear response regime, as demonstrated in a one-dimensional model for multiband superconductors [T. Kamatani , ]. Here we identify the linear coupling term in the Ginzburg-Landau free energy to be the so-called Lifshitz invariant, which takes the form of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mi mathvariant="bold-italic">d</a:mi><a:mo>·</a:mo><a:mo>(</a:mo><a:msubsup><a:mi mathvariant="normal">Ψ</a:mi><a:mi>i</a:mi><a:mo>*</a:mo></a:msubsup><a:mrow><a:mi mathvariant="bold">∇</a:mi></a:mrow><a:msub><a:mi mathvariant="normal">Ψ</a:mi><a:mi>j</a:mi></a:msub><a:mo>−</a:mo><a:msubsup><a:mi mathvariant="normal">Ψ</a:mi><a:mi>j</a:mi><a:mo>*</a:mo></a:msubsup><a:mrow><a:mi mathvariant="bold">∇</a:mi></a:mrow><a:msub><a:mi mathvariant="normal">Ψ</a:mi><a:mi>i</a:mi></a:msub><a:mo>)</a:mo></a:mrow></a:math>, where <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"><i:mi mathvariant="bold-italic">d</i:mi></i:math> is a constant vector and <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"><k:msub><k:mi mathvariant="normal">Ψ</k:mi><k:mi>i</k:mi></k:msub></k:math> and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:msub><m:mi mathvariant="normal">Ψ</m:mi><m:mi>j</m:mi></m:msub><m:mspace width="4pt"/><m:mrow><m:mo>(</m:mo><m:mi>i</m:mi><m:mo>≠</m:mo><m:mi>j</m:mi><m:mo>)</m:mo></m:mrow></m:math> represent superconducting order parameters. We classify all pairs of irreducible representations of order parameters in the crystallographic point groups that allow for the existence of the Lifshitz invariant. We emphasize that the Lifshitz invariant can appear even in systems with inversion symmetry. The results are applied to a model of <p:math xmlns:p="http://www.w3.org/1998/Math/MathML"><p:mi>s</p:mi></p:math>-wave superconductors on a Kagome lattice with various bond orders, for which in some cases we confirm that the Leggett mode appears as a resonance peak in a linear optical conductivity spectrum based on microscopic calculations. We discuss a possible experimental observation of the Leggett mode by a linear optical response in multiband superconductors. Published by the American Physical Society 2024
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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 | 0.003 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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".