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.
Graphene near charge neutrality is expected to behave like a quantum-critical, relativistic plasma—the “Dirac fluid”—in which massless electrons and holes collide at a rapid rate. We used on-chip terahertz spectroscopy to measure the frequency-dependent optical conductivity of clean, micrometer-scale graphene at electron temperatures between 77 and 300 kelvin. At charge neutrality, we observed the quantum-critical scattering rate characteristic of the Dirac fluid. At higher doping, we detected two distinct current-carrying modes with zero and nonzero total momenta, a manifestation of relativistic hydrodynamics. Our work reveals the quantum criticality and unusual dynamic excitations near charge neutrality in graphene.