How to accurately measure the mobility and viscosity of two-dimensional carriers?

Abstract: Two different methods of \emph{metrological} accuracy are proposed to determine the mobility and viscosity of ultra clean two-dimensional electron liquids. The experimental data analysis is based on the Gurzhi hydrodynamic model under no-slip boundary conditions without preliminary assumptions about carrier scattering times. The applicability of no-slip boundary conditions has been proven. A Hall bar with several conducting channels of different widths in a zero magnetic field and a sample with a single channel in a perpendicular field are considered. In both cases, it was possible to accurately isolate the ohmic part of the total measured resistance and, then find the exact mobility and viscosity of the charge liquid. The extracted e-e scattering time is extremely close to that obtained by other experimental group for transport measurements of superballistic point contact. At low temperatures the e-e scattering time demonstrates a stronger dependence compare to $1/T^{2}$ behavior predicted by Fermi liquid theory. We propose both methods as powerful tools for viscometry and finding the mobility of two-dimensional systems.