The hydrodynamic regime of electron transport has been recently realized in conductors with ultralow densities of defects. Although relaxation processes in two-dimensional (2D) fluids have been studied in many theoretical works, the viscosity of the realistic Fermi gas of 2D electrons having a quadratic energy spectrum and interacting by Coulomb's law has not been reliably determined either in theory or in experiment. Here, we construct a theory of viscosity and thermal conductivity in such a system. We compare the calculated viscosity of the 2D electron Fermi gas and the previously known viscosity of a 2D Fermi liquid with available experimental data extracted from the hydrodynamic negative magnetoresistance of the best-quality GaAs quantum wells. Based on this comparison, we argue that measurements of the temperature dependence of the viscosity can allow us to trace the transition between an electron Fermi liquid and a Fermi gas.
A hallmark of electron hydrodynamics---a transport regime dominated by electron collisions---is that collisions enhance conduction and reduce dissipation, causing resistance to drop and conductance to rise with temperature (
T). Here, the authors present a microscopic study of two-dimensional electron fluids, predicting linear-in-
T scaling of hydrodynamic conductance. This behavior, contrasting with the
T2 scaling in three-dimensional Fermi liquids, arises from a cascade of multiple long-lived viscous modes unique to two-dimensional systems. The number of modes relevant for transport grows as
T decreases, resulting in a non-Fermi-liquid linear-in-
T behavior.