Measuring Hall viscosity of graphene’s electron fluid

Electron hydrodynamics in graphene Electrons can move through graphene in a manner reminiscent of fluids, if the conditions are right. Two groups studied the nature of this hydrodynamic flow in different regimes (see the Perspective by Lucas). Gallagher et al. measured optical conductivity using a waveguide-based setup, revealing signatures of quantum criticality near the charge neutrality point. Berdyugin et al. focused on electron transport in the presence of a magnetic field and measured a counterintuitive contribution to the Hall response that stems from hydrodynamic flow. Science, this issue p. 158, p. 162; see also p. 125 The Hall response in graphene can contain a counterintuitive contribution that stems from hydrodynamic flow. An electrical conductor subjected to a magnetic field exhibits the Hall effect in the presence of current flow. Here, we report a qualitative deviation from the standard behavior in electron systems with high viscosity. We found that the viscous electron fluid in graphene responds to nonquantizing magnetic fields by producing an electric field opposite to that generated by the ordinary Hall effect. The viscous contribution is substantial and identified by studying local voltages that arise in the vicinity of current-injecting contacts. We analyzed the anomaly over a wide range of temperatures and carrier densities and extracted the Hall viscosity, a dissipationless transport coefficient that was long identified theoretically but remained elusive in experiments.