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A Nature experiment shows that the number of spin-1 molecular units in a chain controls whether its fractional edge spins couple to a superconductor. Odd-length chains (three to 13 units in the reported set) produce Yu–Shiba–Rusinov states inside the superconducting gap and have a total-spin S = 1 ground state. Even-length chains (four to 14 units) settle into S = 0 and show no corresponding superconducting coupling.
The result demonstrates a length-selectable interaction in molecular Haldane chains, not a working quantum computer. It suggests a possible route to molecular spin qubits, but coherent control, reliable readout and device integration remain unproven.
What the experiment built and measured
Vaxevani, Ortuzar, Trivini and collaborators assembled antiferromagnetically coupled spin-1 triangulene molecules into chains on a proximitized Au(111)/Nb(110) surface. The niobium provides superconductivity while the gold surface supports the molecular structures. Scanning-tunnelling spectroscopy (STS) was then used to resolve both edge-related and bulk excitations.
The study examined chain lengths from N = 3 through N = 14 triangulene units. This finite-size range is important: a Haldane chain has a gapped interior but leaves effective spin-1/2 degrees of freedom at its two ends. In a short molecule, those two edge spins can still interact with each other, and that interaction determines how the whole chain responds to the superconducting substrate.
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Why changing the length changes the coupling
Fractional edge spins in a Haldane chain
Each triangulene unit contributes a spin-1 building block. Antiferromagnetic coupling between neighboring units creates the characteristic Haldane state: the bulk is separated from its lowest magnetic excitations by a gap, while an effective spin-1/2 appears at each open end. These end spins are not isolated in a short chain; their wavefunctions overlap through the interior.
Parity changes the inter-edge exchange
As units are added, the effective exchange between the two edge spins changes in both magnitude and sign. The experiment identifies an odd-even alternation in the resulting ground state. Odd values of N give a global triplet-like S = 1 ground state, leaving a net spin available to interact with the superconductor. Even values give a singlet-like S = 0 ground state, so the chain has no net spin for the same in-gap coupling channel. The authors reproduce this alternation with a two-site model and use higher-energy spin excitations as an independent check.
Odd and even chains show different superconducting signatures
| Chain property | Odd number of units | Even number of units |
|---|---|---|
| Examples in the study | N = 3, 5, 7, 9, 11, 13 | N = 4, 6, 8, 10, 12, 14 |
| Ground-state total spin | S = 1 | S = 0 |
| Subgap response | Yu–Shiba–Rusinov (YSR) bound states inside the superconducting gap | No corresponding superconducting coupling observed |
| Physical interpretation | Inter-edge exchange leaves a net moment that couples to the substrate | Inter-edge exchange forms a nonmagnetic state decoupled from the substrate |
“Decoupled” here describes the measured superconducting response: even chains do not show the in-gap YSR states seen for odd chains. It does not mean that every electronic interaction with the surface vanishes.
What the YSR states mean in this experiment
Yu–Shiba–Rusinov states are localized bound states that appear inside a superconductor’s energy gap when a magnetic moment interacts with the superconducting condensate. In this experiment, STS detects them only for the odd-length chains. Their presence is consistent with the calculated and measured S = 1 ground state of those chains. Even chains lack the required net magnetic moment in their S = 0 ground state, so no analogous in-gap state is detected.
The parity effect therefore links three observations rather than treating the YSR peaks as an isolated spectral feature: chain length fixes the sign and strength of edge-to-edge exchange; that exchange selects the total-spin ground state; and the ground state controls whether a magnetic bound state forms in the superconducting gap.
Bulk and edge excitations provide a cross-check
The edge response is not the only evidence. Even chains show spin-triplet excitations outside the superconducting gap, with energies that decrease as the chain gets longer:
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| Even-chain length | Reported triplet excitation |
|---|---|
| N = 4 | 6.3 meV |
| N = 6 | 3.1 meV |
| N = 8 | 1.9 meV |
| N = 10 | 1.0 meV |
| N = 12 | approximately 0.5 meV |
Weak extra-gap triplet features also appear for odd chains: 2.7 meV at N = 7, 1.6 meV at N = 9, approximately 0.8 meV at N = 11 and approximately 0.5 meV at N = 13. These numbers are spectroscopy energies reported in the extended-data captions of the 2026 Nature article, tied to the stated chain lengths and excitation assignments; they are not universal constants. Together with the larger Haldane gap protecting the bulk, the size-dependent excitations support the interpretation that the low-energy alternation is governed by interacting edge states.
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Could this become a molecular spin qubit?
The authors present length-tunable edge-spin coupling as a possible foundation for qubits made from pi-conjugated carbon molecules. In principle, selecting the chain length could select whether a molecular spin couples to a superconducting environment, offering a way to engineer and probe a localized quantum degree of freedom.
That is a proposed direction, not a demonstrated qubit. The report contains spectroscopy on molecular chains, but no operation of a qubit, coherent gate sequence or quantum-information benchmark. Establishing a practical device would require controlled manipulation of the spin, high-fidelity state readout, coherence under the substrate and measurement environment, reproducible fabrication, and integration into a circuit.
What the result does—and does not—establish
- It establishes an odd-even dependence of molecular-chain coupling to a superconducting substrate over the measured range N = 3–14.
- It identifies odd-chain YSR states with an S = 1 ground state and even-chain absence of that coupling with an S = 0 ground state.
- It supports the explanation using both a two-edge-spin model and independent higher-energy spin excitations.
- It does not establish a commercially available material, a consumer instrument or an operational molecular spin qubit.
The Nature version of record was published on 14 October 2026, with an issue date of 15 October 2026. The molecular chains, proximitized surface and STM/STS measurements are bespoke laboratory systems; data supporting the plots are available from the corresponding author.
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