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Electrical resistance usually originates from lattice imperfections. However, even a perfect
lattice has a fundamental resistance limit, given by the Landauer 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 reveal the details of 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
fundamental limitations of ballistic electrons, with important implications for fundamental science
and future technologies. |