Imaging the crossover between ohmic and hydrodynamic electron flow in graphene with a single spin magnetometer

In conventional conductors, transport is typically dominated by electron-phonon and electron-impurity scattering, giving rise to a direct proportionality between current and electric field known as Ohm’s law. In ultra-clean graphene devices where the momentum-conserving electron-electron interaction dominates, transport is expected to obey hydrodynamics in which the electrons behave like a classical fluid. By measuring the stray magnetic field created by the current flow, we directly image the crossover from ohmic to viscous flow in a high mobility graphene constriction using nitrogen-vacancy center magnetometry. At room temperature, current flow concentrates at the edges of the constriction regardless of carrier density, indicating ohmic transport. However, below 200K, we observe a crossover into the viscous flow where the current concentrates at the center of the constriction. Our imaging technique provides a direct observation of collision-dominated electron transport.