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Tunnelling dynamics between superconducting bound states at the atomic limit


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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Fig. 1: Tunnelling between YSR states.
Fig. 2: Direct versus thermal Shiba–Shiba tunnelling.
Fig. 3: Relaxation channels and regimes.
Fig. 4: Tunnelling dynamics.

Data availability

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.


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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).

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Authors and Affiliations



H.H. did the experiments with support from J.S., R.D., K.K. and C.R.A. C.P., A.L.Y., J.C.C., B.K. and J.A. provided theory support. H.H., C.P. and C.R.A. modelled and analysed the data with support from all authors. All authors discussed the results. H.H. and C.R.A. wrote the manuscript with input from all authors.

Corresponding author

Correspondence to Christian R. Ast.

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Supplementary information

Supplementary Information

Experiment, analysis and theory details and Supplementary Figs. 1–6.

Source data

Source Data Fig. 1

Data of the four dI/dV spectra in Fig. 1d (without cascade offset).

Source Data Fig. 2

Data of the two I(V) spectra in Fig. 2a (T = 10 mK) and Fig. 2b (T = 1 K).

Source Data Fig. 3

Data of the curves in Fig. 3d including: experiment, noise limit, fit 0.3 μeV, ref. 0.15 μeV and ref. 0.6 μeV.

Source Data Fig. 4

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).

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