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Thermalization and dynamics of high-energy quasiparticles in a superconducting nanowire

Nature Physics volume 19, pages 956–960 (2023)Cite this article

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Abstract

The relaxation of energetic quasiparticles in superconducting nanostructures involves many cascaded interactions between electrons, phonons and Cooper pairs. These dynamics are central to the performance of devices such as qubits or photon detectors. However, they are still not well understood, as they require experiments in which quasiparticles are injected in a controlled fashion. Until now, such experiments have typically employed solid-state tunnel junctions with a fixed tunnel barrier. Here we use instead the scanning critical current microscopy technique that we developed by taking advantage of a cryogenic scanning tunnelling microscope to tune independently the energy and the rate of quasiparticle injection through, respectively, the bias voltage and the tunnelling current. For high-energy quasiparticles, we observe a reduction in the critical current of a nanowire and show it is mainly controlled by the injected power and, marginally, by the injection rate. Our results prove a thermal mechanism for the reduction of the critical current and give insight into the rapid dynamics of the generated hot spot.

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Fig. 1: Experimental set-up.
Fig. 2: The critical current as a function of the bias voltage and injected power.
Fig. 3: Scanning critical current microscopy.
Fig. 4: The effect of the power injected by quasiparticles on the electronic temperature.
Fig. 5: Relaxation dynamics of the injected quasiparticles.

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Data availability

The datasets generated and analysed during the current study are available in the Figshare repository at https://doi.org/10.6084/m9.figshare.22093259.v1. All other data that support the findings of this study are available from the corresponding authors upon reasonable request. Source data are provided with this paper.

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Acknowledgements

We thank M. Aprili, T. Cren, M. Houzet, T. Klein, J. Meyer and S. Sankar for fruitful discussions and G. Vinel for help in the software development for the numerical simulation. C.C. acknowledges funding from the French National Research Agency (grant ANR-16-CE30-0019-ELODIS2). E.F.C.D. was supported by the CEA-EUROTALENTS programme. F. L.-B. and E.F.C.D. acknowledge support from the LabEx FOCUS ANR 11-LABX-0013, and F. L.-B. was supported by the EU’s Horizon research and innovation programme under grant agreement no. 800923 (SUPERTED).

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Authors and Affiliations

  1. Université Grenoble Alpes, CEA, Grenoble INP, IRIG-Pheliqs, Grenoble, France

    T. Jalabert, F. Gustavo, J. L. Thomassin & C. Chapelier

  2. Institut de RadioAstronomie Millimétrique (IRAM), Saint Martin d’Hères, France

    E. F. C. Driessen

  3. Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, Grenoble, France

    F. Levy-Bertrand

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  1. T. Jalabert
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Contributions

J.L.T. and F.G. prepared the samples in the cleanroom facility. E.F.C.D. and C.C. pioneered the experiment. T.J. and C.C. performed the measurements reported in this article. T.J. performed the simulations. T.J., E.F.C.D., F.L.-B. and C.C. analysed the data and wrote the manuscript.

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Correspondence to T. Jalabert or C. Chapelier.

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Extended data

Extended Data Fig. 1 Determination of the superconducting gap by tunnelling spectroscopy.

Dots: Differential conductance as a function of bias voltage Vb normalized to its large bias value at T = 100 mK. Red solid line corresponds to BCS fit (see text) with Teff = 556 mK, Δ = 370 μeV and Γin = 0.02 Δ Sample N03.

Source data

Extended Data Fig. 2 Temperature dependence of the density of states.

Sample N06. Left : normalized differential conductance as a function of bias voltage Vb for different temperatures. Each spectrum is normalized to its large bias value. Black solid line corresponds to the critical temperature Tc = 1.39 K. Right : thermal evolution of the superconducting gap. Red solid line corresponds to a BCS fit. The error bars represent the estimated accuracy of the fit.

Source data

Extended Data Fig. 3 Current-voltage characteristics for different injection currents.

The wire current is raised and decreased in order to show the hysteretic loop and determine the critical current Ic and the retrapping current Ir. Dashed line corresponds to the situation where the STM tip is withdrawn (no tunnelling current), and solid lines to It = 100 pA and 2 nA from right to left. All curves are recorded for a constant temperature T = 1.60 K and bias voltage Vb = 200 mV. Sample N07.

Source data

Extended Data Fig. 4 Influence of the injection position on the critical current.

(a) Nanowire shape. (b) Critical current as a function of the STM tip position along the nanowire for different tunnelling conditions at T = 180 mK. (c) Map of the critical current as a function of the injection position at a fixed tunnelling setpoint: It = 500 pA and Vb = 40 mV. Without injection current, \({{{{{\rm{I}}}}}^{0}}_{{{{\rm{c}}}}}\) = 18.5 μA. Sample N06.

Source data

Extended Data Fig. 5 Effect of the injected power on the electronic temperature for injection of quasiparticles in the dead-end strip and in the ground plane.

(a) Schematics of the sample with indicated injection positions. (b) Electronic temperature at the crossing point between the nanowire and the dead-end strip as a function of ItVb for injection in the dead-end strip (circles) and in the ground plane (crosses) at T = 70 mK. Sample N16.

Source data

Extended Data Fig. 6 Phonon contribution to the heat flow.

Voltage threshold at different tunneling currents above which the assumption of a well thermalized phonon bath breaks down. The errors bars are estimated from the bias voltage difference between which the Te(ItVb) curve at a fixed tunneling current still lies on the linear thermal behavior and starts to deviate from it within our experimental resolution.

Source data

Extended Data Fig. 7 Time evolution of the critical current.

Example of a burst of injected quasiparticles, each of them occurring at a time pointed out by a vertical dashed line.

Source data

Extended Data Fig. 8 Relaxation dynamics of the injected quasiparticles for a different recombination time.

Points are the same data as in Fig. 5 of the main text and solid lines are numerical fits with τrel = 40 ps and τrec = 250 ps. The dashed line is the stationary critical current \({{{{{\rm{I}}}}}^{{{{\rm{stat}}}}}}_{{{{\rm{c}}}}}\). The inset is a zoom at low power.

Source data

Extended Data Fig. 9 Relaxation dynamics of the injected quasiparticles for different relaxation times.

Points are the same data as in Figure 5 of the main text, and solid lines are numerical fits with τrel = 20 ps (top) and τrel = 60 ps (down). The dashed line is the stationary critical current \(I^{\mathrm{stat}}_{\mathrm{c}}\). The inset shows a zoom at a low power.

Source data

Extended Data Table 1 Parameters of the samples
Full size table

Supplementary information

Supplementary Information

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Source data

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Jalabert, T., Driessen, E.F.C., Gustavo, F. et al. Thermalization and dynamics of high-energy quasiparticles in a superconducting nanowire. Nat. Phys. 19, 956–960 (2023). https://doi.org/10.1038/s41567-023-01999-4

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