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  • Letter
  • Open Access

Spin-dependent tunneling between individual superconducting bound states

Haonan Huang1, Jacob Senkpiel1, Ciprian Padurariu2, Robert Drost1, Alberto Villas3, Raffael L. Klees4, Alfredo Levy Yeyati3, Juan Carlos Cuevas3, Björn Kubala2 et al.

Joachim Ankerhold2, Klaus Kern1,5, and Christian R. Ast1,*

  • 1Max-Planck-Institut für Festkörperforschung, Heisenbergstraße 1, 70569 Stuttgart, Germany
  • 2Institut für Komplexe Quantensysteme and IQST, Universität Ulm, Albert-Einstein-Allee 11, 89069 Ulm, Germany
  • 3Departamento de Física Teórica de la Materia Condensada and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, 28049 Madrid, Spain
  • 4Fachbereich Physik, Universität Konstanz, 78457 Konstanz, Germany
  • 5Institut de Physique, Ecole Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland

  • *Corresponding author: c.ast@fkf.mpg.de
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Phys. Rev. Research 3, L032008 – Published 8 July, 2021

DOI: https://doi.org/10.1103/PhysRevResearch.3.L032008

Abstract

Magnetic impurities on superconductors induce discrete bound levels inside the superconducting gap, known as Yu-Shiba-Rusinov (YSR) states. YSR levels are fully spin polarized such that the tunneling between YSR states depends on their relative spin orientation. Here, we use scanning tunneling spectroscopy to resolve the spin dynamics in the tunneling process between two YSR states by experimentally extracting the angle between the spins. To this end, we exploit the ratio of thermally activated and direct spectral features in the measurement to directly extract the relative spin orientation between the two YSR states. We find freely rotating spins down to 7 mK, indicating a purely paramagnetic nature of the impurities. Such a noncollinear spin alignment is essential not only for producing Majorana bound states but also as an outlook manipulating and moving the Majorana state onto the tip.

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References (58)

  1. S. H. Pan, E. W. Hudson, K. M. Lang, H. Eisaki, S. Uchida, and J. C. Davis, Imaging the effects of individual zinc impurity atoms on superconductivity in Bi2Sr2CaCu2O8+δ, Nature (London) 403, 746 (2000).
  2. S. Nadj-Perge, I. K. Drozdov, J. Li, H. Chen, S. Jeon, J. Seo, A. H. MacDonald, B. A. Bernevig, and A. Yazdani, Observation of Majorana fermions in ferromagnetic atomic chains on a superconductor, Science 346, 602 (2014).
  3. G. C. Ménard, S. Guissart, C. Brun, R. T. Leriche, M. Trif, F. Debontridder, D. Demaille, D. Roditchev, P. Simon, and T. Cren, Two-dimensional topological superconductivity in Pb/Co/Si(111), Nat. Commun. 8, 2040 (2017).
  4. S. Kezilebieke, R. Zitko, M. Dvorak, T. Ojanen, and P. Liljeroth, Observation of coexistence of Yu-Shiba-Rusinov states and spin-flip excitations, Nano Lett. 19, 4614 (2019).
  5. A. Odobesko, D. Di Sante, A. Kowalski, S. Wilfert, F. Friedrich, R. Thomale, G. Sangiovanni, and M. Bode, Observation of tunable single-atom Yu-Shiba-Rusinov states, Phys. Rev. B 102, 174504 (2020).
  6. S. Kezilebieke, M. N. Huda, V. Vano, M. Aapro, S. C. Ganguli, O. J. Silveira, S. Głodzik, A. S. Foster, T. Ojanen, and P. Liljeroth, Topological superconductivity in a designer ferromagnet-superconductor van der Waals heterostructure, Nature (London) 588, 424 (2020).
  7. L. Yu, Bound state in superconductors with paramagnetic impurities, Acta Phys. Sin 21, 75 (1965).
  8. H. Shiba, Classical spins in superconductors, Prog. Theor. Phys. 40, 435 (1968).
  9. A. I. Rusinov, Superconductivity near a paramagnetic impurity, JETP Lett. 9, 85 (1969).
  10. A. Yazdani, B. A. Jones, C. P. Lutz, M. F. Crommie, and D. M. Eigler, Probing the local effects of magnetic impurities on superconductivity, Science 275, 1767 (1997).
  11. S.-H. Ji, T. Zhang, Y.-S. Fu, X. Chen, X.-C. Ma, J. Li, W.-H. Duan, J.-F. Jia, and Q.-K. Xue, 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).
  12. K. J. Franke, G. Schulze, and J. I. Pascual, Competition of superconducting phenomena and Kondo screening at the nanoscale, Science 332, 940 (2011).
  13. N. Hatter, B. W. Heinrich, D. Rolf, and K. J. Franke, Scaling of Yu-Shiba-Rusinov energies in the weak-coupling Kondo regime, Nat. Commun. 8, 2016 (2017).
  14. L. Malavolti, M. Briganti, M. Hänze, G. Serrano, I. Cimatti, G. McMurtrie, E. Otero, P. Ohresser, F. Totti, M. Mannini, R. Sessoli, and S. Loth, Tunable spin-superconductor coupling of spin 1/2 vanadyl phthalocyanine molecules, Nano Lett. 18, 7955 (2018).
  15. J. Senkpiel, C. Rubio-Verdú, M. Etzkorn, R. Drost, L. M. Schoop, S. Dambach, C. Padurariu, B. Kubala, J. Ankerhold, C. R. Ast, and K. Kern, Robustness of Yu-Shiba-Rusinov resonances in the presence of a complex superconducting order parameter, Phys. Rev. B 100, 014502 (2019).
  16. H. Huang, R. Drost, J. Senkpiel, C. Padurariu, B. Kubala, A. Levy Yeyati, J. C. Cuevas, J. Ankerhold, K. Kern, and C. R. Ast, Quantum phase transitions and the role of impurity-substrate hybridization in Yu-Shiba-Rusinov states, Commun. Phys. 3, 199 (2020).
  17. J. C. Estrada Saldana, A. Vekris, R. Zitko, G. Steffensen, P. Krogstrup, J. Paaske, K. Grove-Rasmussen, and J. Nygard, Two-impurity Yu-Shiba-Rusinov states in coupled quantum dots, Phys. Rev. B 102, 195143 (2020).
  18. H. Kim, A. Palacio-Morales, T. Posske, L. Rózsa, K. Palotás, L. Szunyogh, M. Thorwart, and R. Wiesendanger, Toward tailoring Majorana bound states in artificially constructed magnetic atom chains on elemental superconductors, Sci. Adv. 4, eaar5251 (2018).
  19. A. Kamlapure, L. Cornils, J. Wiebe, and R. Wiesendanger, Engineering the spin couplings in atomically crafted spin chains on an elemental superconductor, Nat. Commun. 9, 3253 (2018).
  20. A. Y. Kitaev, Unpaired Majorana fermions in quantum wires, Phys. Usp. 44, 131 (2001).
  21. J. Alicea, New directions in the pursuit of Majorana fermions in solid state systems, Rep. Prog. Phys. 75, 076501 (2012).
  22. S. Kezilebieke, M. Dvorak, T. Ojanen, and P. Liljeroth, Coupled Yu-Shiba-Rusinov states in molecular dimers on NbSe2, Nano Lett. 18, 2311 (2018).
  23. M. Assig, M. Etzkorn, A. Enders, W. Stiepany, C. R. Ast, and K. Kern, A 10 mK scanning tunneling microscope operating in ultra high vacuum and high magnetic fields, Rev. Sci. Instrum. 84, 033903 (2013).
  24. H. Huang, C. Padurariu, J. Senkpiel, R. Drost, A. L. Yeyati, J. C. Cuevas, B. Kubala, J. Ankerhold, K. Kern, and C. R. Ast, Tunnelling dynamics between superconducting bound states at the atomic limit, Nat. Phys. 16, 1227 (2020).
  25. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.3.L032008 for details on the experiment, theory and data analysis, which includes Refs. [2, 8, 24, 26, 27, 29, 30, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58].
  26. A. V. Balatsky, I. Vekhter, and J. X. Zhu, Impurity-induced states in conventional and unconventional superconductors, Rev. Mod. Phys. 78, 373 (2006).
  27. L. Cornils, A. Kamlapure, L. Zhou, S. Pradhan, A. Khajetoorians, J. Fransson, J. Wiebe, and R. Wiesendanger, Spin-Resolved Spectroscopy of the Yu-Shiba-Rusinov States of Individual Atoms, Phys. Rev. Lett. 119, 197002 (2017).
  28. L. Schneider, P. Beck, J. Wiebe, and R. Wiesendanger, Atomic-scale spin-polarization maps using functionalized superconducting probes, Sci. Adv. 7, eabd7302 (2021).
  29. A. Villas, R. L. Klees, H. Huang, C. R. Ast, G. Rastelli, W. Belzig, and J. C. Cuevas, Interplay between Yu-Shiba-Rusinov states and multiple Andreev reflections, Phys. Rev. B 101, 235445 (2020).
  30. M. Ruby, F. Pientka, Y. Peng, F. von Oppen, B. W. Heinrich, and K. J. Franke, Tunneling Processes into Localized Subgap States in Superconductors, Phys. Rev. Lett. 115, 087001 (2015).
  31. S. Loth, S. Baumann, C. P. Lutz, D. Eigler, and A. J. Heinrich, Bistability in atomic-scale antiferromagnets, Science 335, 196 (2012).
  32. C. R. Ast, B. Jack, J. Senkpiel, M. Eltschka, M. Etzkorn, J. Ankerhold, and K. Kern, Sensing the quantum limit in scanning tunnelling spectroscopy, Nat. Commun. 7, 13009 (2016).
  33. M. H. Devoret, D. Esteve, H. Grabert, G. L. Ingold, H. Pothier, and C. Urbina, Effect of the Electromagnetic Environment on the Coulomb Blockade in Ultrasmall Tunnel-Junctions, Phys. Rev. Lett. 64, 1824 (1990).
  34. D. V. Averin, Y. V. Nazarov, and A. A. Odintsov, Incoherent tunneling of the Cooper pairs and magnetic-flux quanta in ultrasmall Josephson-junctions, Physica B 165-166, 945 (1990).
  35. G. L. Ingold, H. Grabert, and U. Eberhardt, Cooper-pair current through ultrasmall Josephson-junctions, Phys. Rev. B 50, 395 (1994).
  36. F. Pientka, L. I. Glazman, and F. von Oppen, Topological superconducting phase in helical Shiba chains, Phys. Rev. B 88, 155420 (2013).
  37. F. Pientka, L. I. Glazman, and F. von Oppen, Unconventional topological phase transitions in helical Shiba chains, Phys. Rev. B 89, 180505(R) (2014).
  38. S. Hoffman, J. Klinovaja, and D. Loss, Topological phases of inhomogeneous superconductivity, Phys. Rev. B 93, 165418 (2016).
  39. G. M. Andolina and P. Simon, Topological properties of chains of magnetic impurities on a superconducting substrate: Interplay between the Shiba band and ferromagnetic wire limits, Phys. Rev. B 96, 235411 (2017).
  40. J. Klinovaja, P. Stano, A. Yazdani, and D. Loss, Topological Superconductivity and Majorana Fermions in RKKY Systems, Phys. Rev. Lett. 111, 186805 (2013).
  41. M. Vazifeh and M. Franz, Self-Organized Topological State with Majorana Fermions, Phys. Rev. Lett. 111, 206802 (2013).
  42. B. Braunecker and P. Simon, 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).
  43. M. Eschrig, J. Kopu, J. C. Cuevas, and G. Schön, Theory of Half-Metal/Superconductor Heterostructures, Phys. Rev. Lett. 90, 137003 (2003).
  44. S. Sekula and R. Kernohan, Magnetic properties of superconducting vanadium, Phys. Rev. B 5, 904 (1972).
  45. J. Zasadzinski, D. Burnell, E. Wolf, and G. Arnold, Superconducting tunneling study of vanadium, Phys. Rev. B 25, 1622 (1982).
  46. V. Jensen, J. N. Andersen, H. B. Nielsen, and D. L. Adams, The surface-structure of V(100), Surf. Sci. 116, 66 (1982).
  47. R. Koller, W. Bergermayer, G. Kresse, E. L. D. Hebenstreit, C. Konvicka, M. Schmid, R. Podloucky, and P. Varga, The structure of the oxygen induced (1×5) reconstruction of V(100), Surf. Sci. 480, 11 (2001).
  48. F. Dulot, P. Turban, B. Kierren, J. Eugene, M. Alnot, and S. Andrieu, (001)V surface structures analysed by RHEED and STM, Surf. Sci. 473, 172 (2001).
  49. B. Jäck, M. Eltschka, M. Assig, M. Etzkorn, C. R. Ast, and K. Kern, Critical Josephson current in the dynamical Coulomb blockade regime, Phys. Rev. B 93, 020504(R) (2016).
  50. M. T. Randeria, B. E. Feldman, I. K. Drozdov, and A. Yazdani, Scanning Josephson spectroscopy on the atomic scale, Phys. Rev. B 93, 161115(R) (2016).
  51. J. C. Cuevas, A. Martín-Rodero, and A. L. Yeyati, Hamiltonian approach to the transport properties of superconducting quantum point contacts, Phys. Rev. B 54, 7366 (1996).
  52. J.-X. Zhu, Bogoliubov-de Gennes Method and its Applications (Springer, Heidelberg, 2016), Vol. 924.
  53. S. Nadj-Perge, I. K. Drozdov, B. A. Bernevig, and A. Yazdani, Proposal for realizing Majorana fermions in chains of magnetic atoms on a superconductor, Phys. Rev. B 88, 020407(R) (2013).
  54. J. Li, H. Chen, I. K. Drozdov, A. Yazdani, B. A. Bernevig, and A. H. MacDonald, Topological superconductivity induced by ferromagnetic metal chains, Phys. Rev. B 90, 235433 (2014).
  55. A. Heimes, P. Kotetes, and G. Schön, Majorana fermions from Shiba states in an antiferromagnetic chain on top of a superconductor, Phys. Rev. B 90, 060507(R) (2014).
  56. K. Pöyhönen, A. Westström, and T. Ojanen, Topological superconductivity in ferromagnetic atom chains beyond the deep-impurity regime, Phys. Rev. B 93, 014517 (2016).
  57. A. Theiler, K. Björnson, and A. M. Black-Schaffer, Majorana bound state localization and energy oscillations for magnetic impurity chains on conventional superconductors, Phys. Rev. B 100, 214504 (2019).
  58. B. Jäck, Y. Xie, J. Li, S. Jeon, B. A. Bernevig, and A. Yazdani, Observation of a Majorana zero mode in a topologically protected edge channel, Science 364, 1255 (2019).

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Phys. Rev. Research 3, L032008– Published 8 July, 2021
  • Received 17 November 2020
  • Accepted 24 May 2021
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by the Max Planck Society.

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