Revisiting <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>2</mml:mn><mml:mi>π</mml:mi></mml:mrow></mml:math> phase slip suppression in topological Josephson junctions
Bibliographic record
Abstract
Current state-of-the-art devices for detecting and manipulating Majorana fermions commonly consist of networks of Majorana wires and tunnel junctions. We study a key ingredient of these networks---a topological Josephson junction with charging energy---and we pinpoint crucial features for device implementation. The phase-dependent tunneling term contains both the usual $2\ensuremath{\pi}$-periodic Josephson term and a $4\ensuremath{\pi}$-periodic Majorana tunneling term representing the coupling between Majoranas on both sides of the junction. In nontopological junctions when the charging energy is small compared to the Josephson tunneling scale, the low-energy physics is described by $2\ensuremath{\pi}$ phase slips. By contrast, in a topological junction, due to the $4\ensuremath{\pi}$ periodicity of the tunneling term, it is usually expected that only $4\ensuremath{\pi}$ phase slips are possible while $2\ensuremath{\pi}$ phase slips are suppressed. However, we find that if the ratio between the strengths of the Majorana assisted tunneling and the Josephson tunneling is small, as is likely to be the case for many setups, $2\ensuremath{\pi}$ phase slips occur and may even dominate the low-energy physics. In this limit, one can view the $4\ensuremath{\pi}$ phase slips as a pair of $2\ensuremath{\pi}$ phase slips with arbitrarily large separation. We provide an effective description of the system in terms of $2\ensuremath{\pi}$ and $4\ensuremath{\pi}$ phase slips valid for all values of the tunneling ratio. Comparing the spectrum of the effective models with numerical simulations, we determine the crossover between the $4\ensuremath{\pi}$ phase slip regime to the $2\ensuremath{\pi}$ phase slip dominated regime. We also discuss the role of the charging energy as well as the implications of our results on the dissipative phase transitions expected in such a system.
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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 | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.005 | 0.004 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.262 | 0.164 |
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".