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 conductance caused by a finite number of propagating electron modes. This resistance, shown by Sharvin 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, prompting recent theories 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.