There is a limit to the miniaturization of every process, and for charge transport this is realized by the coupling of two single discrete energy levels at the atomic scale. In superconductors, Yu–Shiba–Rusinov (YSR) states are such levels. Here, we place a magnetic impurity on the tip of a scanning tunnelling microscope (YSR-STM) and use it to demonstrate sequential tunnelling of electrons between parity-protected YSR states on the tip and in the sample. Using this Shiba–Shiba tunnelling technique we probe the YSR lifetime, which we can enhance by reducing the relaxation of the excited YSR state to the intrinsic channel. Our work offers a way to characterize and manipulate coupled superconducting bound states, such as Andreev levels, YSR states or Majorana bound states at the atomic limit.
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Source data are provided with this paper. All other data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.
Pillet, J. et al. Andreev bound states in supercurrent-carrying carbon nanotubes revealed. Nat. Phys. 6, 965–969 (2010).
Bretheau, L., Girit, C., Pothier, H., Esteve, D. & Urbina, C. Exciting Andreev pairs in a superconducting atomic contact. Nature 499, 312–315 (2013).
Janvier, C. et al. Coherent manipulation of Andreev states in superconducting atomic contacts. Science 349, 1199–1202 (2015).
Hassler, F., Akhmerov, A. & Beenakker, C. The top-transmon: a hybrid superconducting qubit for parity-protected quantum computation. New J. Phys. 13, 095004 (2011).
Beenakker, C. & Kouwenhoven, L. A road to reality with topological superconductors. Nat. Phys. 12, 618–621 (2016).
Mourik, V. et al. Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices. Science 336, 1003–1007 (2012).
Nadj-Perge, S. et al. Observation of Majorana fermions in ferromagnetic atomic chains on a superconductor. Science 346, 602–607 (2014).
Kim, H. et al. Toward tailoring Majorana bound states in artificially constructed magnetic atom chains on elemental superconductors. Sci. Adv. 4, eaar5251 (2018).
Yu, L. Bound state in superconductors with paramagnetic impurities. Acta Phys. Sin. 21, 75–91 (1965).
Shiba, H. Classical spins in superconductors. Prog. Theor. Phys. 40, 435–451 (1968).
Rusinov, A. I. Superconductivity near a paramagnetic impurity. JETP Lett. 9, 85–87 (1969).
Yazdani, A., Jones, B. A., Lutz, C. P., Crommie, M. F. & Eigler, D. M. Probing the local effects of magnetic impurities on superconductivity. Science 275, 1767–1770 (1997).
Franke, K. J., Schulze, G. & Pascual, J. I. Competition of superconducting phenomena and Kondo screening at the nanoscale. Science 332, 940–944 (2011).
Cornils, L. et al. Spin-resolved spectroscopy of the Yu–Shiba–Rusinov states of individual atoms. Phys. Rev. Lett. 119, 197002 (2017).
Senkpiel, J. et al. Robustness of Yu–Shiba–Rusinov resonances in presence of a complex superconducting order parameter. Phys. Rev. B 100, 014502 (2019).
Heinrich, B. W., Pascual, J. I. & Franke, K. J. Single magnetic adsorbates on s-wave superconductors. Prog. Surf. Sci. 93, 1–19 (2018).
Van der Vaart, N. C. et al. Resonant tunneling through two discrete energy states. Phys. Rev. Lett. 74, 4702–4705 (1995).
Fujisawa, T. et al. Spontaneous emission spectrum in double quantum dot devices. Science 282, 932–935 (1998).
Leggett, A. J. et al. Dynamics of the dissipative two-state system. Rev. Mod. Phys. 59, 1–85 (1987).
Heinrich, A. J., Gupta, J. A., Lutz, C. P. & Eigler, D. M. Single-atom spin-flip spectroscopy. Science 306, 466–469 (2004).
Meier, F., Zhou, L. H., Wiebe, J. & Wiesendanger, R. Revealing magnetic interactions from single-atom magnetization curves. Science 320, 82–86 (2008).
Natterer, F. D. et al. Reading and writing single-atom magnets. Nature 543, 226–228 (2017).
Senkpiel, J.et al. Single channel Josephson effect in a high transmission atomic contact. Preprint at http://arXiv.org/abs/1810.10609 (2018).
Assig, M. et al. A 10 mK scanning tunneling microscope operating in ultra high vacuum and high magnetic fields. Rev. Sci. Instrum. 84, 033903 (2013).
Ast, C. R. et al. Sensing the quantum limit in scanning tunnelling spectroscopy. Nat. Commun. 7, 13009 (2016).
Ruby, M. et al. Tunneling processes into localized subgap states in superconductors. Phys. Rev. Lett. 115, 087001 (2015).
Saldana, J. C. et al. Two-impurity Yu–Shiba–Rusinov states in coupled quantum dots. Preprint at http://arXiv.org/abs/1812.09303 (2018).
Devoret, M. H. et al. Effect of the electromagnetic environment on the Coulomb blockade in ultrasmall tunnel-junctions. Phys. Rev. Lett. 64, 1824–1827 (1990).
Averin, D. V., Nazarov, Y. V. & Odintsov, A. A. Incoherent tunneling of the Cooper pairs and magnetic-flux quanta in ultrasmall Josephson-junctions. Physica B 165-166, 945–946 (1990).
Ingold, G. L. & Nazarov, Y. V. Charge tunneling rates in ultrasmall junctions. Single Charge Tunneling 294, 21–107 (1992).
Ingold, G. L., Grabert, H. & Eberhardt, U. Cooper-pair current through ultrasmall Josephson-junctions. Phys. Rev. B 50, 395–402 (1994).
Zgirski, M. et al. Evidence for long-lived quasiparticles trapped in superconducting point contacts. Phys. Rev. Lett. 106, 257003 (2011).
Olivares, D. G. et al. Dynamics of quasiparticle trapping in Andreev levels. Phys. Rev. B 89, 104504 (2014).
Kozorezov, A. G. et al. Inelastic scattering of quasiparticles in a superconductor with magnetic impurities. Phys. Rev. B 78, 174501 (2008).
Martin, I. & Mozyrsky, D. Nonequilibrium theory of tunneling into a localized state in a superconductor. Phys. Rev. B 90, 100508 (2014).
Dynes, R. C., Narayanamurti, V. & Garno, J. P. Direct measurement of quasiparticle-lifetime broadening in a strong-coupled superconductor. Phys. Rev. Lett. 41, 1509–1512 (1978).
Salkola, M. I., Balatsky, A. V. & Schrieffer, J. R. Spectral properties of quasiparticle excitations induced by magnetic moments in superconductors. Phys. Rev. B 55, 12648–12661 (1997).
Flatte, M. E. & Byers, J. M. Local electronic structure of a single magnetic impurity in a superconductor. Phys. Rev. Lett. 78, 3761–3764 (1997).
Balatsky, A. V., Vekhter, I. & Zhu, J. X. Impurity-induced states in conventional and unconventional superconductors. Rev. Mod. Phys. 78, 373–433 (2006).
Feldman, B. E. et al. High-resolution studies of the Majorana atomic chain platform. Nat. Phys. 13, 286–291 (2017).
This work was funded in part by the ERC Consolidator Grant AbsoluteSpin (grant no. 681164) and by the Center for Integrated Quantum Science and Technology (IQST). J.A. acknowledges funding from the DFG under grant number AN336/11-1. A.L.Y. and J.C.C. acknowledge funding from the Spanish MINECO (grant nos FIS2017-84057-P and FIS2017-84860-R) and from the ‘María de Maeztu’ Programme for Units of Excellence in R&D (MDM-2014-0377).
The authors declare no competing interests.
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Data of the four dI/dV spectra in Fig. 1d (without cascade offset).
Data of the two I(V) spectra in Fig. 2a (T = 10 mK) and Fig. 2b (T = 1 K).
Data of the curves in Fig. 3d including: experiment, noise limit, fit 0.3 μeV, ref. 0.15 μeV and ref. 0.6 μeV.
Data of the curves in Fig. 4b including: right Shiba–Shiba peak area, left Shiba–Shiba peak area, linear reference line, sublinear reference line (square root)—data of the four I(V) spectra in Fig. 4c: 76.9 GΩ, 330 GΩ, 3.45 TΩ, 15.1 TΩ.
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Huang, H., Padurariu, C., Senkpiel, J. et al. Tunnelling dynamics between superconducting bound states at the atomic limit. Nat. Phys. 16, 1227–1231 (2020). https://doi.org/10.1038/s41567-020-0971-0
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