Imaging the breakdown of ohmic transport in graphene

Ohm's law describes the proportionality of current density and electric field. Â In solid-state conductors, Ohm's law emerges due to electron scattering processes that relax the electrical current. Â Here, we use nitrogen-vacancy center magnetometry to directly image the local breakdown of Ohm's law in a narrow constriction fabricated in a high mobility graphene monolayer. Â Ohmic flow is visible at room temperature as current concentration on the constriction edges, with flow profiles entirely determined by sample geometry. Â However, as the temperature is lowered below 200 K, the current concentrates near the constriction center. Â The change in the flow pattern is consistent with a crossover from diffusive to viscous electron transport dominated by electron-electron scattering processes that do not relax current.