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Atomic-scale visualization of electronic fluid flow

Abstract

The most essential characteristic of any fluid is the velocity field, and this is particularly true for macroscopic quantum fluids1. Although rapid advances2,3,4,5,6,7 have occurred in quantum fluid velocity field imaging8, the velocity field of a charged superfluid—a superconductor—has never been visualized. Here we use superconducting-tip scanning tunnelling microscopy9,10,11 to image the electron-pair density and velocity fields of the flowing electron-pair fluid in superconducting NbSe2. Imaging of the velocity fields surrounding a quantized vortex12,13 finds electronic fluid flow with speeds reaching 10,000 km h–1. Together with independent imaging of the electron-pair density via Josephson tunnelling, we visualize the supercurrent density, which peaks above 3 × 107 A cm–2. The spatial patterns in electronic fluid flow and magneto-hydrodynamics reveal hexagonal structures coaligned to the crystal lattice and quasiparticle bound states14, as long anticipated15,16,17,18. These techniques pave the way for electronic fluid flow visualization studies of other charged quantum fluids.

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Fig. 1: Model of quasiparticle and electron-pair tunnelling.
Fig. 2: Quasiparticle tunnelling and electron-pair tunnelling experiments.
Fig. 3: Radial dependence of ρS, Δ02, vS, jS and Φ.
Fig. 4: Visualizing electronic fluid flow.

Data availability

All data are available in the main text, in the Supplementary Information and on Zenodo31. Additional information is available from the corresponding author upon reasonable request.

Code availability

The data analysis computer codes used in this study are available from the corresponding author upon reasonable request.

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Acknowledgements

We thank J. E. Hoffman, H. Suderow and Z. Hadzibabic for helpful discussions and advice. X.L. acknowledges support from the Kavli Institute at Cornell. X.L., Y.X.C., R.S. and J.C.S.D. acknowledge support from the Moore Foundation’s EPiQS Initiative through grant GBMF9457. J.C.S.D. acknowledges support from the Royal Society through award R64897, from Science Foundation Ireland under award SFI 17/RP/5445 and from the European Research Council under award DLV-788932.

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X.L and Y.X.C. carried out the experiments. X.L., Y.X.C. and R.S. developed and implemented the analysis. J.C.S.D. conceived and directed the project. The paper reflects the contributions and ideas of all authors.

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Correspondence to J. C. Séamus Davis.

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The authors declare no competing interests.

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Peer review information Nature Materials thanks Wei Guo and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Supplementary Notes 1–7 and Figs. 1–12.

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Liu, X., Chong, Y.X., Sharma, R. et al. Atomic-scale visualization of electronic fluid flow. Nat. Mater. 20, 1480–1484 (2021). https://doi.org/10.1038/s41563-021-01077-1

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