Detecting Majorana modes in one-dimensional wires by charge sensing
Bibliographic record
Abstract
The electron number parity of the ground state of a semiconductor nanowire proximity coupled to a bulk superconductor can alternate between the quantized values $\ifmmode\pm\else\textpm\fi{}1$ if parameters such as the wire length $L$, the chemical potential $\ensuremath{\mu}$, or the magnetic field $B$ are varied inside the topological superconductor phase. The parity jumps, which may be interpreted as changes in the occupancy of the fermion state formed from the pair of Majorana modes at opposite ends of the wire, are accompanied by jumps $\ensuremath{\delta}N$ in the charge of the nanowire, whose values decrease exponentially with the wire length. We study theoretically the dependence of $\ensuremath{\delta}N$ on system parameters, and compare the locations in the $\ensuremath{\mu}\text{\ensuremath{-}}B$ plane of parity jumps when the nanowire is or is not proximity coupled to a bulk superconductor. We show that, despite the fact that the wave functions of the Majorana modes are localized near the two ends of the wire, the charge-density jumps have spatial distributions that are essentially uniform along the wire length, being proportional to the product of the two Majorana wave functions. We explain how charge measurements, say by an external single-electron transistor, could reveal these effects. Whereas existing experimental methods require direct contact to the wire for tunneling measurements, charge sensing avoids this issue and provides an orthogonal measurement to confirm recent experimental developments. Furthermore, by comparing density of states measurements which show Majorana features at the wire ends with the uniformly distributed charge measurements, one can rule out alternative explanations for earlier results. We shed light on a parameter regime for these wire-superconductor hybrid systems, and propose a related experiment to measure spin density.
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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".