What would establish Majorana zero modes experimentally?

Scope

A convincing Majorana claim needs an explicit target. A zero-energy spectral feature, a measurable fermion parity, coherent control of a small device and a protected non-Abelian operation are different achievements. This selected review connects model expectations to measurements without treating one observable as proof of every later step. It is not an exhaustive census of all platforms or a claim that no future experiment could resolve the question. R1 R2 R3

In superconductors, the relevant objects are emergent quasiparticle modes, not demonstrations of an elementary Majorana particle. A self-adjoint operator can be constructed algebraically from any fermionic operator; experimentally establishing spatially separated, sufficiently isolated zero modes requires more than that change of basis. The ideal chain's boundary states and its bulk phase provide a theoretical benchmark with specified assumptions. R1

Mathematical assumptions

Adopt $\{\gamma_i,\gamma_j\}=2\delta_{ij}$. For $c=(\gamma_1+i\gamma_2)/2$, physical pair parity is $P_{12}=1-2c^\dagger c=-i\gamma_1\gamma_2$. A chosen orientation of an ideal adjacent exchange gives

$$U_i=\exp\left(\frac{\pi}{4}\gamma_{i+1}\gamma_i\right) =\frac{1+\gamma_{i+1}\gamma_i}{\sqrt2}, \qquad U_i\gamma_iU_i^\dagger=\gamma_{i+1}, \quad U_i\gamma_{i+1}U_i^\dagger=-\gamma_i.$$

Reversing orientation reverses the exchange. Ivanov derives a projective braid representation for separated half-quantum vortices in a specified chiral p-wave setting, with adiabatic motion relative to excited core states. Overall phases are disregarded. Fixing total parity leaves $2^{n-1}$ states for $2n$ Majoranas; adjacent exchanges can remain noncommuting within that space. This result does not itself identify a material or verify an experimental control sequence. R2

An original occupation-basis calculation checks four Majoranas, both two-dimensional fixed-parity sectors, unitarity, operator transformations and the braid relations. Two exchange orders give distinct states, with squared overlap $1/2$ for the selected initial vacuum, yet identical occupation probabilities in that readout basis. An appropriate analysis basis is needed to distinguish them. The same example gives equal probabilities for a cross-pair parity measurement in both a coherent preparation and a mixed state. Thus a 50/50 histogram alone is not a unique fusion signature. These are ideal algebraic examples, with no spatial device, noise or experimental data simulated.

Experimental criteria

Spectroscopy must be assessed against alternatives. Pan and Das Sarma's model study compares topological, inhomogeneity-induced and disorder-induced zero-bias structures. It motivates testing dependence on barriers, fields and gates rather than classifying a device from a single favorable trace. The selected evidence does not supply a universal numerical classifier that uniquely identifies topology from conductance alone. R3

A practical review should retain the entire inference chain: calibrated observables, a device model, controls against competing states, and sensitivity to analysis choices. Bulk and end measurements, controlled perturbations, parity readout and operation tests supply complementary evidence. This is an editorial validation framework, not a theorem that a particular checklist is sufficient. Models and measurements must refer to the same device regime. R1 R3

What recent devices establish

Aghaee and colleagues' 2025 InAs–Al experiment demonstrates interferometric single-shot parity measurement. The authors explicitly retain a finely tuned low-energy Andreev-state alternative, alongside constraints imposed by coupling to both ends. Optimized readout assignment error does not equal the error of a quantum gate. The result establishes a readout capability within the paper's stated limits. R4

Van Loo and colleagues' paper, published online on 11 February 2026, measures parity through quantum capacitance in a minimal InSb–Al chain and reports lifetimes exceeding a millisecond. The selected author version describes limited protection in a two-site device. That lifetime characterizes parity stability; it is not automatically a coherence time or a demonstrated braiding operation. R5

Ten Haaf and colleagues probe all three sites of an InSbAs quantum-dot chain. Their selected post-review manuscript connects outer-site zero-bias peaks with a middle-site excitation gap, controlled by superconducting phase. Detuning responses differ between gapped and gap-closed settings, supporting the finite-chain model. The measured couplings are not independently tunable in every sweep. Three sites allow a useful end–middle comparison, but do not establish asymptotic protection of a long chain. R6

Luethi and colleagues supply a complementary theoretical caution. In their microscopic dot–superconductor model, some short-chain states resembling poor man's Majoranas evolve into trivial states under uniform extension. Robustness to chemical-potential perturbations or a large excitation gap alone does not remove this ambiguity. Uniform extension is a theoretical diagnostic; real devices may have nonuniform parameters. This does not independently reclassify the experimental device above. R7

A dated coherent-control advance

The 10 July 2026 preprint by Zatelli and colleagues reports coherent parity oscillations in coupled minimal Kitaev chains. Comparing even and odd manifolds helps test residual splitting that could cancel in only one manifold. A selected trace has frequency $106.7\pm0.4$ MHz and exponential Rabi decay $26\pm2$ ns. The authors interpret the sweet-spot behavior as partial protection; no journal acceptance was verified for this review. R8

The preprint explicitly separates these operations from topologically protected gates: lifting the degeneracy to perform the rotation is not protected independently of chain length. Reported population leakage is not a measured gate fidelity. Longer-chain protection scaling, fusion tests and braiding are further objectives. Coherent rotation is meaningful progress, while a claim about exchange statistics requires evidence about the implemented operation. R8

Limits and disputes

Nature published a transport-gap critique and an associated reply online on 24 June 2026. Their identities and dates were checked, but the final full texts were not accessible in this review. Both are linked without deciding which analysis is correct. Their existence must not be presented as a retraction of the 2025 parity paper. R9 R10

Retraction status requires a separate, specific record. The 2018 quantized-conductance article discussed in the Majorana overview has a 2021 retraction notice; that is a different publication from the 2025 readout experiment. Keep notices attached to the exact article. Full supplements, raw-data checks, broad platform comparisons and independent experimental replication remain outside this selected review. R11 R4

Discovery implications

For candidate selection, retain promising signals together with their alternatives and operating conditions. For quantum operations, ask which preparation, control and measurement distinguish the proposed transformation from ordinary dynamics, readout bias or an incoherent mixture. Increasing device length or showing a favorable oscillation is useful only with an explicit error and protection analysis. These are proposed review priorities; neither this article nor its ideal algebra constitutes certification of a topological qubit. R1 R3

Related topics

Continue with Majorana models and readout, topological material candidates, and experimental methods.

Material cases

No sample-specific material records are included in this article. Model results are not experimental transition temperatures.