Imaging the breakdown of ohmic transport in graphene

Ohm's law describes the proportionality of current density and
electric field.  In solid-state conductors, Ohm's law
emerges due to electron scattering processes that relax the electrical
current.  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.
 Ohmic flow is visible at room temperature as current
concentration on the constriction edges, with flow profiles entirely
determined by sample geometry.  However, as the temperature is
lowered below 200 K, the current concentrates near the constriction
center.  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.