Electron viscosity, current vortices and negative nonlocal resistance in graphene

Quantum-critical strongly correlated electron systems are predicted to feature universal collision-dominated transport resembling that of viscous fluids(1-4). However, investigation of these phenomena has been hampered by the lack of known macroscopic signatures of electron viscosity(5-9). Here we identify vorticity as such a signature and link it with a readily verifiable striking macroscopic d.c. transport behaviour. Produced by the viscous flow, vorticity can drive electric current against an applied field, resulting in a negative nonlocal voltage. We argue that the latter may play the same role for the viscous regime as zero electrical resistance does for superconductivity. Besides offering a diagnostic that distinguishes viscous transport from ohmic currents, the sign-changing electrical response affords a robust tool for directly measuring the viscosity-to-resistivity ratio. A strongly interacting electron-hole plasma in high-mobility graphene(10-12) affords a unique link between quantum-critical electron transport and the wealth of fluid mechanics phenomena.