Fractional Spins in Molecular Chains Couple to a Superconductor Only When the Chain Is Odd

Physicists have long been fascinated by a strange promise hidden inside certain magnetic materials: the ability of a chain of ordinary spins to split itself into half-spins that live only at its ends. Now a team of researchers has brought that promise into contact with one of the most delicate states of matter in physics, a superconductor, and discovered that the meeting obeys a surprisingly strict rule. Whether the fractional edge spins of a molecular chain talk to the superconducting condensate depends entirely on whether the chain contains an odd or an even number of building blocks. The finding, published in Nature, turns a philosophical curiosity about quantum matter into a tunable design principle for future quantum devices.

The work was carried out by Katerina Vaxevani, Jon Ortuzar, Stefano Trivini and colleagues under the supervision of Jose Ignacio Pascual, spanning the CIC nanoGUNE research center in Donostia-San Sebastián, the University of Santiago de Compostela, and partner institutions across Europe. Their subject was a Haldane chain, a one-dimensional array of spin-1 units coupled antiferromagnetically, meaning each unit tries to align opposite to its neighbors. In 1983, Duncan Haldane predicted that such chains possess a topological energy gap protecting their interior, while their boundaries are forced to host spin-1/2 excitations, half the spin of any constituent. These fractional edge states are not impurities or defects; they are an unavoidable consequence of the chain’s topology, as robust as the chain itself.

For decades, Haldane’s prediction belonged mostly to the realm of bulk crystals and theoretical elegance. The rise of on-surface synthesis changed that. Chemists can now assemble chains of polycyclic aromatic hydrocarbons atom by atom on metal surfaces, and triangulene, a triangular graphene fragment with a net spin of 1, has emerged as an ideal spin-1 unit. When triangulene molecules are fused into chains, their spins couple antiferromagnetically, and scanning tunneling microscopy can directly image and probe the fractional spins at the ends. The Spanish-led team pushed this chemistry one step further by growing the chains not on an ordinary metal but on a thin gold film sitting atop niobium, a superconductor. The gold layer inherits superconductivity through the proximity effect, giving the researchers a superconducting stage on which to place their topological chains.

The central question was deceptively simple: does the fractionalization survive when the chain is placed on a superconductor? Superconductors abhor magnetism. A magnetic impurity on an s-wave superconductor breaks Cooper pairs and binds quasiparticles into localized in-gap states known as Yu-Shiba-Rusinov states, named after the three theorists who described them in the 1960s. These states are exquisitely sensitive to the spin of the impurity, its exchange coupling to the electrons, and the total spin of the ground state. If the fractional edge spins of a Haldane chain could be made to form such states, the chain would become a hybrid spin-superconductor system in which topology and superconductivity coexist, a combination highly sought after in quantum information research.

Using scanning tunneling spectroscopy at 1.2 kelvin, the team measured chains of varying lengths, from three triangulene units up to fourteen. The spectra revealed a striking alternation. Chains with an odd number of units displayed Yu-Shiba-Rusinov bound states inside the superconducting gap, signaling that the chain’s ground state carries a total spin of S = 1 and couples to the condensate. Chains with an even number of units showed no such in-gap states; instead, their ground state is a nonmagnetic singlet, S = 0, which is essentially invisible to the superconductor. The parity of the chain length, odd or even, acts as a switch that turns the coupling to superconductivity on and off.

The origin of this alternation lies in the interaction between the two fractional edge spins. In a finite chain, the spin-1/2 end states are not infinitely far apart; they communicate through the chain and form either a singlet or a triplet depending on the sign and strength of their effective coupling. In short antiferromagnetic Heisenberg chains, this even-odd effect is well known: an odd number of spin-1 units leaves an uncompensated S = 1 ground state, while an even number pairs the edges into an S = 0 singlet. The researchers captured the physics with a minimal two-site model treating the two edge spins and their mutual exchange, and the model’s predictions matched the tunneling spectra, including additional spin excitation peaks appearing outside the superconducting gap that independently confirmed the sign of the inter-edge interaction.

The spectroscopy also revealed the collective many-body excitations of the chain interior. Triplet and quintet spin states, as well as higher-energy collective modes, appeared in the spectra at energies set by the Haldane gap, which is much larger than the superconducting gap. Because these excitations lie far above the superconducting energy scale, they remain decoupled from the condensate, protected by the topological gap. This separation of energy scales is crucial: it means the superconductor perturbs only the low-energy edge physics while the bulk of the chain retains its topological character. The team even demonstrated control over individual edge spins by removing a terminal hydrogen atom with the microscope tip, which passivates one edge and converts the spectrum of the opposite end, shifting the Yu-Shiba-Rusinov state and eliminating singlet-triplet features in a manner consistent with freeing the remaining edge spin.

Quantitatively, the edge spins were found to sit in the weak-coupling regime, with an exchange interaction to the superconductor much smaller than the superconducting gap itself. The Yu-Shiba-Rusinov binding energies measured across chains of different lengths ranged from a few tenths of a millielectronvolt down to values approaching the gap edge, tracking the length-dependent evolution of the edge-spin coupling. The spatial maps showed that the in-gap spectral weight is concentrated around the zigzag periphery of the terminal triangulene units, exactly where the fractional spin resides. This spatial and energetic consistency leaves little doubt that the superconductor is sensing genuine fractional spin-1/2 objects rather than ordinary localized moments.

The implications reach toward quantum technology. The authors and theorists elsewhere have pointed out that the singlet-triplet pair formed by the edge spins of a Haldane chain constitutes a natural spin qubit, and that the topological protection of the edge states could shield quantum information from local noise. The new result shows that this qubit can be coupled to, or decoupled from, a superconducting environment simply by choosing the chain length, and that the coupling strength can be tuned through the weak-coupling regime where spin excitations enjoy long lifetimes. Because the chains are built from pi-conjugated carbon architectures, they are chemically versatile and potentially integrable with existing superconducting circuits built on niobium and gold platforms.

There are, of course, steps remaining before such visions become hardware. The experiments were performed at cryogenic temperatures on single chains addressed by a scanning tunneling microscope, and extending the platform to electrical contacts, longer chains, and arrays will demand substantial engineering. Yet the conceptual achievement stands on its own: fractional quantum numbers, once a hallmark of abstract topology, have been shown to exchange quantum information with a superconducting condensate in a controllable, parity-dependent way. A chain of molecules, each no wider than a nanometer, now offers a knob that alternates between magnetic and silent with every added unit, a small switch with potentially large consequences for the architecture of quantum machines.

Subject of Research: Parity-dependent coupling of fractional edge spins in molecular Haldane chains to a proximitized superconductor

Article Title: Parity-dependent coupling of molecular spin chains to a superconductor

Article References: Vaxevani, K., Ortuzar, J., Trivini, S., Monninger, G., Wang, D., Vilas-Varela, M., Gómez-Rodrigo, L., Peña, D., & Pascual, J. I. (2026). Parity-dependent coupling of molecular spin chains to a superconductor. Nature, 658(8136), 617-622. https://doi.org/10.1038/s41586-026-11117-y

Image Credits: AI Generated

DOI: 10.1038/s41586-026-11117-y

Keywords: Haldane chains, triangulene, fractional edge states, superconductivity, Yu-Shiba-Rusinov states, scanning tunneling spectroscopy, spin-1 chains, topological quantum matter, proximity effect, spin qubits, on-surface synthesis, quantum magnetism