Probing topological degeneracy on a torus using superconducting altermagnets
Bibliographic record
Abstract
The notion of topological order (TO) can be defined through the characteristic ground state degeneracy of a system placed on a manifold with non-zero genus $g$, such as a torus. This ground state degeneracy has served as a key tool for identifying TOs in theoretical calculations but it has never been possible to probe experimentally because fabricating a device in the requisite toroidal geometry is generally not feasible. Here we discuss a practical method that can be used to overcome this difficulty in a class of topologically ordered systems that consist of a TO and its time reversal conjugate $\overline{\rm TO}$. The key insight is that a system possessing such ${\rm TO}\otimes\overline{\rm TO}$ order fabricated on an annulus behaves effectively as TO on a torus, provided that one supplies a symmetry-breaking perturbation that gaps out the edge modes. We illustrate this general principle using a specific example of a spin-polarized $p_x\pm ip_y$ chiral superconductor which is closely related to the Moore-Read Pfaffian fractional quantum Hall state. Specifically, we introduce a simple model with altermagnetic normal state which, in the presence of an attractive interaction, hosts a helical $(p_x-ip_y)^\uparrow\otimes(p_x+ip_y)^\downarrow$ superconducting ground state. We demonstrate that when placed on an annulus with the appropriate symmetry-breaking edge perturbation this planar two-dimensional system, remarkably, exhibits the same pattern of ground state degeneracy as a $p_x+ ip_y$ superconductor on a torus. We discuss broader implications of this behavior and ways it can be tested experimentally.
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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 | 0.000 | 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".