Quantitative measurement of viscosity in two-dimensional electron fluids

Abstract: Electron hydrodynamics is an emerging framework that describes dynamics of interacting electron systems as conventional fluids. While evidence for hydrodynamic-like transport is reported in a variety of two-dimensional materials, precise quantitative measurement of the core parameter, electron viscosity, remains challenging. In this work, we demonstrate that magnetoresistance in Corbino-shaped graphene devices offers a simultaneous Ohmmeter/viscosometer, allowing us to disentangle the individual Ohmic and viscous contributions to the transport response, even in the mixed flow regime. Most surprising, we find that in both monolayer and bilayer graphene, the effective electron-electron scattering rate scales linearly with temperature, at odds with the expected $T$-squared dependence expected from conventional Fermi liquid theory, but consistent with a recently identified tomographic flow regime, which was theoretically conjectured to be generic for two-dimensional charged fluids.