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 Landauer 1 conductance caused by a finite number of propagating electron modes. This resistance, shown by Sharvin 2 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 phenomena 3 – 18 , prompting recent theories 19 , 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.