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Imaging hydrodynamic electrons flowing without Landauer–Sharvin resistance


Electrical resistance usually originates from lattice imperfections. However, even a perfect lattice has a fundamental resistance limit, given by the Landauer1 conductance caused by a finite number of propagating electron modes. This resistance, shown by Sharvin2 to appear at the contacts of electronic devices, sets the ultimate conduction limit of non-interacting electrons. Recent years have seen growing evidence of hydrodynamic electronic phenomena3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18, prompting recent theories19,20 to ask whether an electronic fluid can radically break the fundamental Landauer–Sharvin limit. Here, we use single-electron-transistor imaging of electronic flow in high-mobility graphene Corbino disk devices to answer this question. First, by imaging ballistic flows at liquid-helium temperatures, we observe a Landauer–Sharvin resistance that does not appear at the contacts but is instead distributed throughout the bulk. This underpins the phase-space origin of this resistance—as emerging from spatial gradients in the number of conduction modes. At elevated temperatures, by identifying and accounting for electron–phonon scattering, we show the details of the purely hydrodynamic flow. Strikingly, we find that electron hydrodynamics eliminates the bulk Landauer–Sharvin resistance. Finally, by imaging spiralling magneto-hydrodynamic Corbino flows, we show the key emergent length scale predicted by hydrodynamic theories—the Gurzhi length. These observations demonstrate that electronic fluids can dramatically transcend the fundamental limitations of ballistic electrons, with important implications for fundamental science and future technologies.

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Fig. 1: Landauer–Sharvin bulk geometrical resistance and the experimental setup for its measurement.
Fig. 2: Imaging the Landauer–Sharvin bulk resistance in a Corbino disk.
Fig. 3: Observation of the perfect elimination of Landauer–Sharvin bulk resistance by hydrodynamic electron flow.
Fig. 4: Imaging spiralling magneto-hydrodynamic electron flow and its Gurzhi boundary layer.

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 Source data are provided with this paper. Additional data that support the plots and other analysis in this work are available from the corresponding author upon request.


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We thank L. Ella, G. Falkovich, L. Levitov, M. Polini, M. Shavit, A. Rozen, A. V. Shytov and U. Zondiner for useful discussions. Work was supported by the Leona M. and Harry B. Helmsley Charitable Trust grant, ISF grant (no. 1182/21), Minerva grant (no. 713237), Hydrotronics (no. 873028) and the ERC-Cog (See-1D-Qmatter, no. 647413). T.S. acknowledges the support of the Natural Sciences and Engineering Research Council of Canada (NSERC), in particular the Discovery Grant (no. RGPIN-2020-05842), the Accelerator Supplement (no. RGPAS-2020-00060) and the Discovery Launch Supplement (no. DGECR-2020-00222). During the preparation of this manuscript, we became aware of a partially related STM work17, which images voltage drops in flows across a constriction.

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Authors and Affiliations



C.K., J.B., J.A.S, A.K.G. and S.I. designed the experiment. C.K., J.B. and J.A.S. performed the experiments. J.B. and D.P. fabricated the devices. C.K., J.B., J.A.S. and S.I. analysed the data. T.S., A.S. and S.I. wrote the theoretical model. K.W. and T.T. supplied the hBN crystals. C.K., J.B., A.S. and S.I. wrote the manuscript with input from other authors.

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Correspondence to S. Ilani.

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Nature thanks Yonglong Xie 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 Sections 1–18: Device fabrication; transport measurements; angular symmetry of the measured flow; measurement of the point-spread function (PSF) of the imaging experiments; determining the contact transparency from the measured resistance profile; determining the momentum-relaxing mean-free path over the full temperature range; additional data at a different carrier density; imaging measurements on a second Corbino device; comparing resistance profiles at different temperatures but with similar lMR; the Irrelevance of bulk magneto-resistance contributions; measurement of the Hall angle profile at T = 180 K; temperature dependence of lee; derivation of equation (1) in the main text; Boltzmann simulations of interacting flow in a Corbino geometry; temperature dependence of the outer contact resistance; the dependence of the number of conduction modes on radius in a Corbino device; the physical significance of the resistance function R(r) and accuracy in R(r) measurements from Nanotube SET sensitivity. Supplementary Figures 1–12 and additional references.

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Kumar, C., Birkbeck, J., Sulpizio, J.A. et al. Imaging hydrodynamic electrons flowing without Landauer–Sharvin resistance. Nature 609, 276–281 (2022).

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