Topological <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>d</mml:mi><mml:mo>+</mml:mo><mml:mi>s</mml:mi></mml:mrow></mml:math> wave superconductors in a multiorbital quadratic band touching system
Bibliographic record
Abstract
Realization of topological superconductors is one of the most important goals in studies of topological phases in quantum materials. In this work we theoretically propose a way to attain topological superconductors with nontrivial Fermi surfaces of Bogoliubov quasiparticles. Considering the interacting Luttinger model with $j=3/2$ electrons, we investigate the dominant superconducting channels for a multiorbital quadratic band touching system with finite chemical potential, which breaks the particle-hole symmetry in the normal state. Notably, while the system generally favors $d$-wave pairing, the absence of the particle-hole symmetry necessarily induces $s$-wave pairing and such emergence of $s$-wave pairing leads to new types of topological $d+s$ wave superconductors and selects particular $d$-wave pairing channels. Based on the Landau theory with SO(3) symmetry, we demonstrate that two kinds of topological superconductors are energetically favored; uniaxial nematic phase with secondary $s$-wave pairing (${d}_{3{z}^{2}\ensuremath{-}{r}^{2}}+s$) and time-reversal-symmetry broken phase with secondary $s$-wave pairing $({d}_{3{z}^{2}\ensuremath{-}{r}^{2}}+{d}_{xy}+i{d}_{{x}^{2}\ensuremath{-}{y}^{2}}+s)$. These superconductors contain either nodal lines or Fermi pockets of gapless Bogoliubov quasiparticles and moreover exhibit topological invariants, leading to nontrivial surface states such as drumheadlike surface states or Fermi arcs. We discuss applications of our theory to relevant families of materials, especially half-Heusler compound YPtBi, and suggest possible future experiments.
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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 | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.017 | 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".