Viscosity of two-dimensional electrons

P. S. Alekseev, A. P. Dmitriev

Published 2020-07-05Version 1

The hydrodynamic regime of electron transport has been recently realized in conductors with ultra-low densities of defects. Although many theoretical works have been devoted to studies of relaxation processes in two-dimensional (2D) electron fluids, the viscosity of the realistic Fermi gas of 2D electrons interacting by Coulomb's law has not been reliably determined up to now either in theory or in experiment. Here we construct a theory of viscosity and thermal conductivity in such system. We compare the previously known viscosity of a 2D Fermi liquid and our result for the viscosity of a 2D electron Fermi gas with available experimental data extracted from the hydrodynamic negative magnetoresistance observed on the best-quality GaAs quantum wells. Based on a good agreement between theory and experiment, we conclude that measurements of the temperature dependence of the viscosity is a direct method (i) to identify the hydrodynamic regime of electron transport and (ii) to trace the transition between an electron Fermi liquid and a Fermi gas.