Precision determination of mobility and viscosity of two-dimensional charged fluid

Two different methods of metrological accuracy are proposed to determine the mobility and viscosity of ultraclean 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 more precisely the mobility and viscosity of the charge liquid. The extracted e–e scattering time is close to that obtained by other experimental group from transport measurements of superballistic point contact. At low temperatures, the e–e scattering time demonstrates 1/T2 behavior predicted by Fermi liquid theory. We propose both methods as powerful tools for viscometry and for finding the mobility of two-dimensional systems.