Probing Maximal Viscous Response of Electronic System at the Onset of Fluidity

Electron hydrodynamics has emerged recently as a new paradigm of correlated electron transport in solids, describing phenomena dominated by particle collisions.At the lengthscales exceeding the collision mean free path $l_{\rm ee}$, such systems can be treated as macroscopic fluids. In contrast, when the system size is comparable to $l_{\rm ee}$, the hydrodynamic approach is inapplicable, and the single-particle kinetic treatment is required. Here we bridge the two extremes describing the ballistic-to-viscous crossover in two-dimensional electronic systems. Graphene is a convenient platform for this inquiry, owing to its temperature- and gate-tunable $l_{\rm ee}$. We predict that the crossover manifests itself in a peculiar spatial dependence of the current-induced potential that peaks (reaches its most negative value) at distances comparable to $l_{\rm ee}$, and report the experimental observation of this anomalous behavior at the onset of the fluid state.