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.
This is a preview of subscription content, access via your institution
Access options
Access Nature and 54 other Nature Portfolio journals
Get Nature+, our best-value online-access subscription
$29.99 / 30 days
cancel any time
Subscribe to this journal
Receive 12 print issues and online access
$259.00 per year
only $21.58 per issue
Buy this article
- Purchase on Springer Link
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
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.
References
Leggett, A. J. Quantum Liquids: Bose Condensation and Cooper Pairing in Condensed-Matter Systems (Oxford Univ. Press, 2006).
Zhang, T. & Van Sciver, S. W. Large-scale turbulent flow around a cylinder in counterflow superfluid 4He (He(ii)). Nat. Phys. 1, 36–38 (2005).
Bewley, G. P., Lathrop, D. P. & Sreenivasan, K. R. Visualization of quantized vortices. Nature 441, 588 (2006).
Guo, W. et al. Visualization study of counterflow in superfluid 4He using metastable helium molecules. Phys. Rev. Lett. 105, 045301 (2010).
Guo, W. et al. Visualization of two-fluid flows of superfluid helium-4. Proc. Natl Acad. Sci. USA 111, 4653–4658 (2014).
Fisher, S. N. et al. Andreev reflection, a tool to investigate vortex dynamics and quantum turbulence in 3He-B. Proc. Natl Acad. Sci. USA 111, 4659–4666 (2014).
Kumar, A. et al. Minimally destructive, Doppler measurement of a quantized flow in a ring-shaped Bose–Einstein condensate. N. J. Phys. 19, 025001 (2016).
Seo, S. W. et al. Observation of vortex-antivortex pairing in decaying 2D turbulence of a superfluid gas. Sci. Rep. 7, 4587 (2017).
Hamidian, M. H. et al. Detection of a Cooper-pair density wave in Bi2Sr2CaCu2O8+x. Nature 532, 343–347 (2016).
Cho, D. et al. A strongly inhomogeneous superfluid in an iron-based superconductor. Nature 571, 541–545 (2019).
Liu, X., Chong, Y. X., Sharma, R. & Davis, J. C. S. Discovery of a Cooper-pair density wave state in a transition-metal dichalcogenide. Science 372, 1447–1452 (2021).
Abrikosov, A. A. The magnetic properties of superconducting alloys. J. Phys. Chem. Solids 2, 199–208 (1957).
Rosenstein, B. & Li, D. Ginzburg-Landau theory of type II superconductors in magnetic field. Rev. Mod. Phys. 82, 109–168 (2010).
Hess, H. F., Robinson, R. B. & Waszczak, J. V. Vortex-core structure observed with a scanning tunneling microscope. Phys. Rev. Lett. 64, 2711–2714 (1990).
Klein, U. Microscopic calculations on the vortex state of type II superconductors. J. Low. Temp. Phys. 69, 1–37 (1987).
Norman, M. R. Mean-field superconductivity in a strong magnetic field. Physica C 196, 43–47 (1992).
Gygi, F. & Schlüter, M. Self-consistent electronic structure of a vortex line in a type-II superconductor. Phys. Rev. B 43, 7609–7621 (1991).
Rainer, D., Sauls, J. A. & Waxman, D. Current carried by bound states of a superconducting vortex. Phys. Rev. B 54, 10094–10106 (1996).
Bandurin, D. A. et al. Negative local resistance caused by viscous electron backflow in graphene. Science 351, 1055–1058 (2016).
Crossno, J. et al. Observation of the Dirac fluid and the breakdown of the Wiedemann-Franz law in graphene. Science 351, 1058–1061 (2016).
Moll, P. J. W. et al. Evidence for hydrodynamic electron flow in PdCoO2. Science 351, 1061–1064 (2016).
Levitov, L. & Falkovich, G. Electron viscosity, current vortices and negative nonlocal resistance in graphene. Nat. Phys. 12, 672–676 (2016).
Berdyugin, A. I. et al. Measuring Hall viscosity of graphene’s electron fluid. Science 364, 162–165 (2019).
Yip, S. K. & Sauls, J. A. Nonlinear Meissner effect in CuO superconductors. Phys. Rev. Lett. 69, 2264–2267 (1992).
Volovik, G. E. Superconductivity with lines of GAP nodes: density of states in the vortex. J. Exp. Theor. Phys. Lett. 58, 469–473 (1993).
Wu, H. & Sauls, J. A. Majorana excitations, spin and mass currents on the surface of topological superfluid 3He-B. Phys. Rev. B 88, 184506 (2013).
Anchenko, Y. M. I. & Zil’Berman, L. A. The Josephson effect in small tunnel contacts. J. Exp. Theor. Phys. 55, 2395–2402 (1969).
Ingold, G.-L., Grabert, H. & Eberhardt, U. Electron-pair current through ultrasmall Josephson junctions. Phys. Rev. B 50, 395–402 (1994).
Naaman, O., Teizer, W. & Dynes, R. C. Fluctuation dominated Josephson tunneling with a scanning tunneling microscope. Phys. Rev. Lett. 87, 097004 (2001).
Fulde, P. in Tunneling Phenomena in Solids (eds Burstein, E. & Lundqvist, S.) Ch. 29 (Springer, 1969).
Liu, X., Chong, Y. X., Sharma, R. & Davis, J. C. S. Data associated with ‘Atomic-scale visualization of electronic fluid flow’. Zenodo https://doi.org/10.5281/zenodo.5048540 (2021).
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.
Author information
Authors and Affiliations
Contributions
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.
Corresponding author
Ethics declarations
Competing interests
The authors declare no competing interests.
Additional information
Peer review information Nature Materials thanks Wei Guo and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary information
Supplementary Information
Supplementary Notes 1–7 and Figs. 1–12.
Rights and permissions
About this article
Cite this article
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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/s41563-021-01077-1
This article is cited by
-
Rotating curved spacetime signatures from a giant quantum vortex
Nature (2024)
-
Single-electron charge transfer into putative Majorana and trivial modes in individual vortices
Nature Communications (2023)
-
Detection of a pair density wave state in UTe2
Nature (2023)
-
Magnetic field orientation dependence of planar tunneling spectroscopy in the superconducting state of NbSe2
Quantum Frontiers (2023)