Imaging Hydrodynamic Electrons Flowing Without a 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 of its discrete 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 flows in high-mobility graphene Corbino disk devices to answer this question. First, by imaging ballistic flows at low 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, we identify and account for the contribution of electron-phonon scattering, thus revealing the purely hydrodynamic flow. Strikingly, we find that electron hydrodynamics eliminates the bulk Landauer-Sharvin resistance. Finally, by imaging spiraling magneto-hydrodynamic Corbino flows we reveal the key emergent length-scale predicted by hydrodynamic theories – the Gurzhi length. These observations demonstrate that electronic fluids can dramatically transcend the limitations of ballistic electrons, with important implications for fundamental science and future technologies.