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Parity-dependent coupling of molecular spin chains to a superconductor

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Data availability

All data that support the plots in this paper and other findings of this study are available from the corresponding author. Data analysis was done with WsXM54 and SpectraFox55.

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Acknowledgements

We thank L. Edens for technical support and J. Wolf for help with the substrate growth. We also thank the Quantum-Probe Microscopy group for helpful discussions.

Funding

This research was financed by MCIN/AEI/10.13039/501100011033 and the European Regional Development Fund (ERDF) through grant nos. PID2022-140845OB-C61, PID2022-140845OB-C62 and CEX2020-001038-M, by Xunta de Galicia (Centro de Investigación do Sistema Universitario de Galicia, 2023–2027, grant number ED431G 2023/03) and by the European Union Horizon 2020 and HE programmes through FET-Open project SPRING (no. 863098), the ERC Synergy Grant MolDAM (no. 951519) and the ERC-AdG CONSPIRA (no. 101097693). K.V. acknowledges support from MCIN/AEI/10.13039/501100011033 through PhD scholarship PRE2022-102887. J.O. acknowledges support from the Basque Government through PhD scholarship PRE_2021_1_0350. D.W. acknowledges support from ‘Juan de la Cierva’ grant FJC2020-043831-I financed by MCIN/AEI/10.13039/501100011033 and by the European Union NextGenerationEU/PRTR, as well as from NSFC project no. 12474474.

Author information

Author notes

  1. These authors contributed equally: Katerina Vaxevani, Jon Ortuzar, Stefano Trivini

Authors and Affiliations

  1. CIC nanoGUNE - BRTA, Donostia-San Sebastián, Spain

    Katerina Vaxevani, Jon Ortuzar, Stefano Trivini, Georg Monninger, Dongfei Wang & Jose Ignacio Pascual

  2. Quantronics group, Service de Physique de l’État Condensé (CNRS, UMR 3680), IRAMIS, CEA-Saclay, Université Paris-Saclay, Gif-sur-Yvette, France

    Jon Ortuzar

  3. School of Physics, Beijing Institute of Technology, Beijing, China

    Dongfei Wang

  4. Centro Singular de Investigación en Química Biolóxica e Materiais Moleculares (CiQUS) and Departamento de Química Orgánica, Universidad de Santiago de Compostela, Santiago de Compostela, Spain

    Manuel Vilas-Varela, Lucía Gómez-Rodrigo & Diego Peña

  5. Oportunius, Galician Innovation Agency (GAIN), Santiago de Compostela, Spain

    Diego Peña

  6. Ikerbasque, Basque Foundation for Science, Bilbao, Spain

    Jose Ignacio Pascual

Authors

  1. Katerina Vaxevani
  2. Jon Ortuzar
  3. Stefano Trivini
  4. Georg Monninger
  5. Dongfei Wang
  6. Manuel Vilas-Varela
  7. Lucía Gómez-Rodrigo
  8. Diego Peña
  9. Jose Ignacio Pascual

Contributions

J.I.P. conceived of and supervised the project. M.V.-V. and L.G.-R. synthesized the molecular precursors in solution under the supervision of D.P. K.V., G.M. and D.W. developed the superconducting substrate and grew the triangulene chains. J.O., S.T. and G.M. performed the STM/STS measurements. K.V., J.O., S.T. and G.M. analysed the data. J.O. developed the theoretical model and simulations. J.I.P. wrote the manuscript, with input from K.V., J.O. and S.T. All authors discussed the results and contributed to the final manuscript.

Corresponding author

Correspondence to Jose Ignacio Pascual.

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Competing interests

The authors declare no competing interests.

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Peer review information

Nature thanks Ping Yu and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

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Extended data figures and tables

Extended Data Fig. 1 Results for N = 3 and N = 4 [3]-triangulene chains.

a, Bond-resolved current image of triangulene chain with three units (V = 5 mV, constant-height at tunnel resistance RT ≈ 16 MΩ). b, Low-energy dI/dV spectra over the termini. Dashed grey line is a reference spectrum on the Au(111) substrate. Spectra on the chain termini show YSR peaks developing inside the dGSJ excitations. c, Bond-resolved current image of triangulene chain with four units (V = 8.5 mV, constant-height at RT ≈ 16 MΩ). d, Low-energy dI/dV spectra over the termini. Dashed grey line is a reference spectrum on the Au(111) substrate. Spectra on the chain termini show peaks at about 8.5 meV, corresponding to ST excitations with energy EST = 6.3 meV. e, Differential conductance map at the peak energy, measured simultaneously to the image in c, showing larger conductance over the edge triangulene units.

Extended Data Fig. 2 Results for a N = 5 [3]-triangulene chain.

a, Bond-resolved current image of triangulene chain with five units (V = 5 mV, constant-height at RT ≈ 16 MΩ). b, Low-energy dI/dV spectra over the termini. Dashed grey line is a reference spectrum on the Au(111) substrate. Spectra on the chain termini show YSR states developing from the dGSJ peaks and TS excitation peaks, shown in c. c, Long-range dI/dV spectra averaged at several positions over the edge and the bulk of the triangulene chain in a. d, Differential conductance maps of the triangulene chain in a. The maps are chosen at bias values of the YSR peak, the negative differential resistance (NDR) dip after the dGSJ peaks, the TS excitation and two CS excitation steps, respectively. Both c and d were obtained from a spectral grid over the whole triangulene chain.

Extended Data Fig. 3 Results for N = 6 and N = 7 [3]-triangulene chains.

a, Bond-resolved current image of triangulene chain with six units (V = 5 mV, constant-height at RT ≈ 16 MΩ). b, Low-energy dI/dV spectra over the termini. Dashed grey line is a reference spectrum on the Au(111) substrate. Spectra on the chain termini show ST excitation peaks with EST = 3.1 meV. c, Bond-resolved current image of triangulene chain with seven units (V = 5 mV, constant-height at RT ≈ 16 MΩ). d, Low-energy dI/dV spectra over the termini. Dashed grey line is a reference spectrum on the Au(111) substrate. Spectra on the chain termini show YSR excitation peaks developing inside the gap between dGSJ peaks. Weak TS excitation peaks are observed outside the gap, with ETS = 2.7 meV.

Extended Data Fig. 4 Results for a N = 8 [3]-triangulene chain.

a, Constant-current image of triangulene chain with eight units (V = 5 mV). b, Low-energy dI/dV spectra over the termini. Dashed grey line is a reference spectrum on the Au(111) substrate. Spectra on the chain termini show ST excitation peaks with EST = 1.9 meV. c, Comparison of spin excitation spectra for two distinct N = 8 chains. Both host the many-body S = 1 spin excitations in the same frequencies. The peak at about 35 meV is related to the vibrations of the CO at the scanning tunnelling microscope tip.

Extended Data Fig. 5 Results for N = 9 and N = 10 [3]-triangulene chains.

a, Bond-resolved current image of triangulene chain with nine units (V = 5 mV, constant-height at RT ≈ 16 MΩ). b, Low-energy dI/dV spectra over the termini. Dashed grey line is a reference spectrum on the Au(111) substrate. Spectra on the chain termini show YSR excitation peaks developing inside the dGSJ excitations. Weak TS excitation peaks are observed outside the gap, with ETS = 1.6 meV. c, Bond-resolved current image of triangulene chain with 10 units (V = 5 mV, constant-height at RT ≈ 16 MΩ). d, Low-energy dI/dV spectra over the termini. Dashed grey line is a reference spectrum on the Au(111) substrate. Spectra on the chain termini show ST excitation peaks with EST = 1.0 meV.

Extended Data Fig. 6 Results for a N = 11 [3]-triangulene chain.

a, Low-energy dI/dV spectra over both termini of the N = 11 triangulene chain in Fig. 2d. b, Low-energy dI/dV spectra over both termini of another N = 11 triangulene chain with less YSR bound energy δEYSR. In both plots, the insets are bond-resolved images and dashed grey lines are reference spectra on the Au(111) substrate. Both chains show weak TS excitation shoulders as marked, with ETS ≈ 0.8 meV, the one in b with larger peak amplitude. c, Spatial distribution of YSR peak amplitude and TS onset over the top-end triangulene in a, obtained from a 20 × 20 spectral grid. Both signals are distributed around the zigzag periphery, with similar shape at both polarities.

Extended Data Fig. 7 Results for N = 12 and N = 13 [3]-triangulene chains.

a, Bond-resolved current image of triangulene chain with 12 units (V = 5 mV, constant-height at RT ≈ 16 MΩ). b, Low-energy dI/dV spectra over the termini. Dashed grey line is a reference spectrum on the Au(111) substrate. Spectra on the chain termini show faint ST excitation peaks with EST ≈ 0.5 meV. The dGSJ resonances appear with particle–hole asymmetry characteristic of YSR states with finite Coulomb potential scattering. Here we attribute it to the incipient emergence of YSR states, still overlapping with the quasiparticle peaks of the film. c, Bond-resolved current image of triangulene chain with 13 units (V = 5 mV, constant-height at RT ≈ 16 MΩ). d, Low-energy dI/dV spectra over the termini. Dashed grey line is a reference spectrum on the Au(111) substrate. Spectra on the chain termini show YSR excitation peaks developing inside the dGSJ excitations. Spectra on the chain termini show faint TS excitation peaks with ETS ≈ 0.5 meV.

Extended Data Fig. 8 Results for a N = 14 [3]-triangulene chain.

a, Bond-resolved current image of triangulene chain with 14 units (V = 5 mV, constant-height at RT ≈ 16 MΩ). b, Low-energy dI/dV spectra over the termini. Dashed grey line is a reference spectrum on the Au(111) substrate. In the inset, we show the scaled components of the dGSJ states for each termini, to emphasize the peak components owing to YSR state.

Extended Data Fig. 9 Edge state passivation by dehydrogenation of a terminal triangulene, N = 14.

a, Bond-resolved current STM image of the N = 14 chain. The insets show a zoomed image of the end triangulene unit n = 14 before and after applying a bias pulse over the marked C site. The pulse produces dehydrogenation of the targeted C site, after which the triangulene appears with characteristic orbital shape in the images (V = 5 mV). b, Differential conductance spectra on the end unit n = 1 before and after the dehydrogenation in a. The YSR peak of Extended Data Fig. 8 over the n = 1 triangulene shifts to a binding energy δEYSR = 0.36 meV when the opposite end is dehydrogenated (V = 5 mV, I = 500 pA). c, Differential conductance spectral map versus tip–sample resistance over the n = 1 triangulene unit. The YSR state shifts towards the gap edges and merges with dGSJ resonances as the tip approaches, indicating that the edge spin lies in the weak interaction regime (JK ≪ Δ; Supplementary Information section 5).

Extended Data Fig. 10 Edge state passivation by dehydrogenation of a terminal triangulene, N = 8.

a, Constant-current STM image of a N = 8 chain before and after dehydrogenation of the lower triangulene end. b, Comparison of spectra on the top triangulene before and after the dehydrogenation in a. The passivation of the lower edge state leads to disappearance of ST features and the emergence of an in-gap YSR state. As shown in Supplementary Information section 4, the H atom removal removes intra-chain exchange correlations and results in a free-like edge spin on the opposite end.

Extended Data Fig. 11 STM image and dI/dV spectra of the surface of a 25-monolayer Au(111) film.

a, STM image of the surface of a 25-monolayer Au(111) film, exhibiting the herringbone reconstruction. b, dI/dV spectra measured at 1.2 K, showing the characteristic onset of its surface state close to −0.5 V sample bias. This value is close to the surface state onset on bulk Au(111) substrates.

Supplementary information

Supplementary Information (download PDF )

This file contains five supplementary figures, further references and the following sections: 1. Deconvolution of the superconducting tip gap and YSR bound state energies; 2. Spin model of the S = 1 chain; 3. Two-site model of YSR excitations in fractional spin end states; 4. Theoretical analysis of the tip-induced passivation of fractional spin end states; and 5. Determination of interaction regime with the superconductor.

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Vaxevani, K., Ortuzar, J., Trivini, S. et al. Parity-dependent coupling of molecular spin chains to a superconductor. Nature 658, 617–622 (2026). https://doi.org/10.1038/s41586-026-11117-y

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