Abstract

The quantum coupling of fully different degrees of freedom is a challenging path towards new functionalities for quantum electronics1,2,3. Here we show that the localized classical spin of a magnetic atom immersed in a superconductor with a two-dimensional electronic band structure gives rise to a long-range coherent magnetic quantum state. We experimentally evidence coherent bound states with spatially oscillating particle–hole asymmetry extending tens of nanometres from individual iron atoms embedded in a 2H–NbSe2 crystal. We theoretically elucidate how reduced dimensionality enhances the spatial extent of these bound states and describe their energy and spatial structure. These spatially extended magnetic states could be used as building blocks for coupling coherently distant magnetic atoms in new topological superconducting phases4,5,6,7,8,9,10,11.

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References

  1. 1.

    et al. Coupling a single trapped atom to a nanoscale optical cavity. Science 340, 1202–1205 (2013).

  2. 2.

    et al. Strain-mediated coupling in a quantum dot-mechanical oscillator hybrid system. Nature Nanotech. 9, 106–110 (2014).

  3. 3.

    et al. Observation of Majorana fermions in ferromagnetic atomic chains on a superconductor. Science 346, 602–607 (2014).

  4. 4.

    , , & Proposal for realizing Majorana fermions in chains of magnetic atoms on a superconductor. Phys. Rev. B 88, 020407(R) (2013).

  5. 5.

    , , & Majorana fermions emerging from magnetic nanoparticles on a superconductor without spin–orbit coupling. Phys. Rev. B 84, 195442 (2011).

  6. 6.

    , & Two-dimensional p-wave superconducting states with magnetic moments on a conventional s-wave superconductor. Phys. Rev. B 88, 180503(R) (2013).

  7. 7.

    & Interplay between classical magnetic moments and superconductivity in quantum one-dimensional conductors: Toward a self-sustained topological Majorana phase. Phys. Rev. Lett. 111, 147202 (2013).

  8. 8.

    , , & Topological superconductivity and Majorana fermions in RKKY systems. Phys. Rev. Lett. 111, 186805 (2013).

  9. 9.

    & Self-organized topological state with Majorana fermions. Phys. Rev. Lett. 111, 206802 (2013).

  10. 10.

    , & Topological superconducting phase in helical Shiba chains. Phys. Rev. B 88, 155420 (2013).

  11. 11.

    , , , & Helical order in one-dimensional magnetic atom chains and possible emergence of Majorana bound states. Phys. Rev. B 90, 060401(R) (2014).

  12. 12.

    Bound state in superconductors with paramagnetic impurities. Acta Phys. Sin. 21, 75–91 (1965).

  13. 13.

    Classical spins in superconductors. Prog. Theor. Phys. 40, 435–451 (1968).

  14. 14.

    Superconductivity near a paramagnetic impurity. JETP Lett. 9, 85–87 (1969).

  15. 15.

    , & Electron-tunneling observation of impurity bands in superconducting manganese-implanted lead. Phys. Rev. Lett. 47, 1163–1165 (1981).

  16. 16.

    , & Impurity-induced states in conventional and unconventional superconductors. Rev. Mod. Phys. 78, 373–433 (2006).

  17. 17.

    , , , & Probing the local effects of magnetic impurities on superconductivity. Science 275, 1767–1770 (1997).

  18. 18.

    et al. High-resolution scanning tunneling spectroscopy of magnetic impurity induced bound states in the superconducting gap of Pb thin films. Phys. Rev. Lett. 100, 226801 (2008).

  19. 19.

    , & Competition of superconducting phenomena and Kondo screening at the nanoscale. Science 332, 940–944 (2011).

  20. 20.

    et al. Fermi surface of 2H–NbSe2 and its implications on the charge-density-wave mechanism. Phys. Rev. B 64, 235119 (2001).

  21. 21.

    & Local spectrum of a superconductor as a probe of interactions between magnetic impurities. Phys. Rev. B 61, 14810–14814 (2000).

  22. 22.

    et al. Tunneling processes into localized subgap states in superconductors. Phys. Rev Lett. 115, 087001 (2015).

  23. 23.

    et al. Superconductivity in one-atomic-layer metal films grown on Si(111). Nature Phys. 6, 104–108 (2010).

  24. 24.

    et al. Remarkable effects of disorder on superconductivity of single atomic layers of lead on silicon. Nature Phys. 10, 444–450 (2014).

  25. 25.

    et al. Interface-induced high-temperature superconductivity in single unit-cell FeSe films on SrTiO3. Chin. Phys. Lett. 29, 037402 (2012).

  26. 26.

    & Topological superconductivity and high Chern numbers in 2D ferromagnetic Shiba lattices. Phys. Rev. Lett. 114, 236803 (2015).

  27. 27.

    & On the structural properties of the Nb1+xSe2 phase. Acta Chem. Scand. 18, 697–706 (1964).

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Acknowledgements

This work was supported by the French Agence Nationale de la Recherche through the contracts ANR Electrovortex and ANR Mistral. G.C.M. acknowledges funding from the CFM foundation providing his PhD grant. V.S.S. thanks L. R. Tagirov for his assistance. The authors thank E. Canadell, K. Behnia and V. Vinokur for stimulating discussions.

Author information

Affiliations

  1. Institut des Nanosciences de Paris, Sorbonne Universités, UPMC Univ Paris 6 and CNRS-UMR 7588, F-75005 Paris, France

    • Gerbold C. Ménard
    • , Christophe Brun
    • , Stéphane Pons
    • , Vasily S. Stolyarov
    • , François Debontridder
    • , Matthieu V. Leclerc
    • , Dimitri Roditchev
    •  & Tristan Cren
  2. Laboratoire de Physique des Solides, Université Paris-Sud, 91405 Orsay, France

    • Sébastien Guissart
    •  & Pascal Simon
  3. Laboratoire de physique et d’étude des matériaux, LPEM-UMR8213/CNRS-ESPCI ParisTech-UPMC, 10 rue Vauquelin 75005 Paris, France

    • Stéphane Pons
    •  & Dimitri Roditchev
  4. Moscow Institute of Physics and Technology, 141700 Dolgoprudny, Russia

    • Vasily S. Stolyarov
  5. Institut des Matériaux Jean Rouxel, CNRS Université de Nantes, UMR 6502, 2 rue de la Houssinière, BP32229, 44322 Nantes, France

    • Etienne Janod
    •  & Laurent Cario

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Contributions

D.R., T.C. and F.D. designed the experiments. G.C.M., C.B., T.C., D.R., V.S.S., M.V.L. and S.P. carried out the experiments. G.C.M. and T.C. processed and analysed the data. S.G. and P.S. performed the theoretical modelling. L.C. and E.J. grew the samples and performed the chemical analysis. All authors discussed the results and took part in the correction of the manuscript.

Competing interests

The authors declare no competing financial interests.

Corresponding authors

Correspondence to Pascal Simon or Tristan Cren.

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https://doi.org/10.1038/nphys3508

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