Electron viscosity, current vortices and negative nonlocal resistance in graphene

Abstract

In analogy to fluids, electric currents can exhibit viscosity — albeit with effects difficult to observe experimentally. Now, vorticity is reported as a signature feature of electron viscosity in graphene, which leads to negative nonlocal resistance. Quantum-critical strongly correlated electron systems are predicted to feature universal collision-dominated transport resembling that of viscous fluids1,2,3,4. However, investigation of these phenomena has been hampered by the lack of known macroscopic signatures of electron viscosity5,6,7,8,9. 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 graphene10,11,12 affords a unique link between quantum-critical electron transport and the wealth of fluid mechanics phenomena.