Imaging the Breaking of Electrostatic Dams in Graphene for Ballistic and Viscous Fluids

Under special conditions the conduction of electrical current through a material can mimic the flow of a viscous fluid. This so-called 'hydrodynamic' regime occurs when the rate of momentum-conserving collisions between charge carriers is larger than the momentum-relaxing rate due to other scattering sources. Ultraclean graphene has emerged as an ideal platform for studying hydrodynamic flow, leading to the possibility of directly imaging fluid-like behaviors with high-resolution experimental probes. In this work, we use scanning tunneling potentiometry to resolve the nanometer-scale flow of electrons in graphene as they pass through channels defined by smooth and tunable p-n junction barriers. We observe that as the sample temperature and channel widths are increased, the electronic flow undergoes a Knudsen-to-Gurzhi transition from a ballistic to viscous regime characterized by a channel conductance that exceeds the ballistic limit, as well as suppressed charge accumulation against the barriers. Our results are successfully modelled by finite-element simulations of two-dimensional viscous current flow, and they illustrate how electronic fluid flow evolves with carrier density, channel width, and temperature.