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Two different methods of \emph{metrological} accuracy are proposed todetermine the mobility and viscosity of ultra clean two-dimensional electronliquids. The experimental data analysis is based on the Gurzhi hydrodynamicmodel under no-slip boundary conditions without preliminary assumptions aboutcarrier scattering times. The applicability of no-slip boundary conditions hasbeen proven. A Hall bar with several conducting channels of different widths ina zero magnetic field and a sample with a single channel in a perpendicularfield are considered. In both cases, it was possible to accurately isolate theohmic part of the total measured resistance and, then find the exact mobilityand viscosity of the charge liquid. The extracted e-e scattering time isextremely close to that obtained by other experimental group for transportmeasurements of superballistic point contact. At low temperatures the e-escattering time demonstrates a stronger dependence compare to $1/T^{2}$behavior predicted by Fermi liquid theory. We propose both methods as powerfultools for viscometry and finding the mobility of two-dimensional systems.

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