Electronic structure of topological superconductors in the presence of a vortex lattice
Bibliographic record
Abstract
Certain types of topological superconductors and superfluids are known to host protected Majorana zero modes in cores of Abrikosov vortices. When such vortices are arranged in a dense periodic lattice one expects zero modes from neighboring vortices to hybridize and form dispersing bands. Understanding the structure of these bands is essential for the schemes that aim to employ the zero modes in quantum computation applications and in studies of their strongly interacting phases. We investigate here the band formation phenomenon in two concrete models, describing a two-dimensional ${p}_{x}+i{p}_{y}$ superconductor and a superconducting surface of a three-dimensional strong topological insulator (Fu-Kane model), using a combination of analytical and numerical techniques. We find that the physics of the Majorana bands is well described by tight-binding models of Majorana fermions coupled to a static ${Z}_{2}$ gauge field with a nontrivial gauge flux through each plaquette, in accord with expectations based on very general arguments. In the case of the Fu-Kane model we also find that, irrespective of the lattice geometry, the Majorana band becomes completely flat at the so-called neutrality point (chemical potential coincident with the Dirac point) where the model exhibits an extra chiral symmetry. In this limit the low-energy physics will be dominated by four-fermion interaction terms which are permitted by symmetries and may arise from the Coulomb interaction between the constituent electron degrees of freedom.
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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 | 0.000 | 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) | 0.000 | 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".