Majorana Platforms and Evidence Standards

No single zero-bias anomaly uniquely identifies a Majorana zero mode. Andreev bound states, quantum-dot singlet–doublet crossings, Kondo resonances, disorder-induced class-D peaks, weak antilocalization, and instrumental or selection effects can produce overlapping signatures. A strong platform claim therefore requires a calibrated gapped regime, correlated signals at separated boundaries, robustness and scaling predicted by one forward model, explicit trivial comparators, reproducibility across devices, and ultimately parity operations or non-Abelian protocols that the alternatives cannot emulate.

Evidence cutoff. This synthesis covers sources available through 10 August 2026. Device-level status is mutable; new data, corrections, retractions, or independent reanalyses can change the ceiling. For results, corrections, and supersession notes after that date, use the dated Quantum Matter and Emergence Research synthesis.

Required background. Topological BdG boundary modes supplies the model-level invariant and wavefunctions. Flux and Josephson dynamics supplies parity and periodicity caveats.

Helpful background. Model selection supplies the likelihood and held-out-test framework.

Evidence ladder

Each rung needs the preceding rungs; none can be replaced by a more dramatic local feature.

1. Calibrated ingredients. Establish the parent gap, spin–orbit and Zeeman scales, electrostatic occupancy, temperature, tunnel couplings, disorder bounds, and measurement transfer function.
2. Subgap state. Demonstrate a reproducible low-energy state over a declared parameter region with raw conductance, backgrounds, resolution, and full sweep selection.
3. Topological bulk compatibility. Show gap closing and reopening or another bulk-sensitive transition diagnostic under a forward model that includes trivial Andreev bands and inhomogeneity.
4. Nonlocal boundary pair. Correlate both ends, length scaling, charge response, and local perturbations; a local zero mode is insufficient.
5. Parity dynamics. Measure parity lifetime, poisoning, state preparation, and readout fidelity while ruling out ordinary charge or dot states.
6. Non-Abelian operation. Demonstrate path-order-dependent transformations with controls that distinguish braiding or measurement-only fusion from dynamical phases and calibrated unitary gates.

The zero-temperature $2e^2/h$ resonant-Andreev value in an ideal single-channel lead is a useful quantitative target, but finite temperature, dissipation, extra channels, and tunnel coupling change the line shape. Conversely, smooth confinement and disorder can produce near-quantized trivial peaks. Prada et al. 2020, §§3–6 reviews this continuity, and Pan and Das Sarma 2020 gives explicit disorder-induced alternatives.

Platform-specific alternatives

Semiconductor nanowires and planar junctions. Smooth potentials create partially separated Andreev states; quantum dots generate singlet–doublet crossings; strong disorder creates class-D spectral accumulation. Orbital fields can close the parent gap before the ideal Zeeman criterion is met. Measure both ends, the nonlocal gap, charge response, length dependence, and response to deliberately moved local gates.

Magnetic chains and vortices. Yu–Shiba–Rusinov bands, ordinary vortex levels, tip-induced shifts, and unresolved level spacing can mimic a zero mode. Map spatial decay and spin structure, establish the bulk or substrate gap, vary chain length or vorticity, and fit the complete spectrum rather than the zero-energy pixel.

Quantum-dot Kitaev chains and islands. Short “poor man’s Majorana” chains can realize finely tuned zero modes and parity degrees of freedom without the exponential topological protection of a long gapped phase. The three-site experiment of Bordin et al. 2025 found enhanced robustness relative to two sites while explicitly noting absent phase control. van Loo et al. 2026 demonstrated single-shot parity readout in a minimal chain; that is an important operation, but the experiment’s own “minimal” setting must not be silently upgraded to long-chain topological protection or non-Abelian braiding.

Current ceiling and supersession record

The evidence record contains an important negative control. A 2018 claim of quantized Majorana conductance was retracted in 2021 after reanalysis no longer supported quantization; the Zhang et al. 2021 retraction notice is part of the source chain, not optional history.

The 2025 interferometric parity-readout report by Microsoft Azure Quantum 2025 used a transport tune-up to designate an allegedly topological regime; the paper itself states that parity readout alone does not distinguish a topological Majorana state from a suitably tuned trivial Andreev state. A 2026 Nature Matters Arising analysis reported that the underlying regions appeared disordered and gapless and argued that trivial mechanisms remained viable; it also linked the underlying data and reproducing code Legg 2026, pp. E22–E26. The appropriate ceiling as of the cutoff is therefore:

Several platforms have produced controlled subgap states, nonlocal and parity-sensitive measurements, and improving engineered Kitaev-chain behavior. These are substantial platform advances. The ensemble of publicly documented evidence does not yet justify treating a generic zero-bias feature, a transport tune-up, parity readout in a minimal chain, or a single device family as a unique demonstration of spatially protected Majorana zero modes and non-Abelian braiding.

This statement is deliberately platform- and date-bounded. It does not deny the model, nor does it pre-judge future experiments that pass the ladder.

The validity map shows the adversarial exits that remain open at each rung.

Local zero-bias evidence is the beginning of model comparison, not its end. A protected Majorana claim requires a gapped calibrated regime, spatial and parity structure, independent reproducibility, and operations that survive explicit trivial alternatives. Original schematic, not to scale; evidence cutoff 10 August 2026.

The complete paired-matter claim test matrix provides the semantic equivalent.

Exercise

Evaluate a hypothetical anomaly. A single tunnel contact shows a robust near-zero peak over magnetic field, but the opposite end was not measured and the parent gap softens. What is licensed, and what is the next decisive test?

Solution

The data license a reproducible local subgap state in the measured region, subject to temperature and resolution calibration. They do not establish a gapped topological bulk or paired end modes. The next experiment should measure a full two-ended conductance matrix and a bulk-sensitive gap proxy under the same gate and field sweep, with local gates used to test whether the two ends respond nonlocally. Fits must include smooth-potential Andreev states, a dot or Kondo model where relevant, and disorder-induced class-D states. If the gap is absent, the claimed protected regime fails before parity or braiding interpretation.

References

• Bordin, A., Liu, C.-X., Dvir, T., Zatelli, F., ten Haaf, S. L. D., van Driel, D., Wang, G., van Loo, N., Zhang, Y., Wolff, J. C., Van Caekenberghe, T., Badawy, G., Gazibegovic, S., Bakkers, E. P. A. M., Wimmer, M., Kouwenhoven, L. P., and Mazur, G. P. (2025). “Enhanced Majorana stability in a three-site Kitaev chain.” Nature Nanotechnology 20, 726–731. doi:10.1038/s41565-025-01894-4.
• Legg, H. F. (2026). “On the robustness of topological gap detection via transport.” Nature 654, E22–E26. doi:10.1038/s41586-026-10567-8.
• Microsoft Azure Quantum. (2025). “Interferometric single-shot parity measurement in InAs–Al hybrid devices.” Nature 638, 651–655. doi:10.1038/s41586-024-08445-2.
• Pan, H., and Das Sarma, S. (2020). “Physical mechanisms for zero-bias conductance peaks in Majorana nanowires.” Physical Review Research 2, 013377. doi:10.1103/PhysRevResearch.2.013377.
• Prada, E., San-Jose, P., de Moor, M. W. A., Geresdi, A., Lee, E. J. H., Klinovaja, J., Loss, D., Nygård, J., Aguado, R., and Kouwenhoven, L. P. (2020). “From Andreev to Majorana bound states in hybrid superconductor–semiconductor nanowires.” Nature Reviews Physics 2, 575–594. doi:10.1038/s42254-020-0228-y.
• van Loo, N., Zatelli, F., Steffensen, G. O., Roovers, B., Wang, G., Van Caekenberghe, T., Bordin, A., van Driel, D., Zhang, Y., Huisman, W. D., Badawy, G., Bakkers, E. P. A. M., Mazur, G. P., Aguado, R., and Kouwenhoven, L. P. (2026). “Single-shot parity readout of a minimal Kitaev chain.” Nature 650, 334–339. doi:10.1038/s41586-025-09927-7.
• Zhang, H., Liu, C.-X., Gazibegovic, S., Xu, D., Logan, J. A., Wang, G., van Loo, N., Bommer, J. D. S., de Moor, M. W. A., Car, D., Op het Veld, R. L. M., van Veldhoven, P. J., Koelling, S., Verheijen, M. A., Pendharkar, M., Pennachio, D. J., Shojaei, B., Lee, J. S., Palmstrøm, C. J., Bakkers, E. P. A. M., Das Sarma, S., and Kouwenhoven, L. P. (2021). “Retraction note: Quantized Majorana conductance.” Nature 591, E30. doi:10.1038/s41586-021-03373-x.