Linear-in-temperature conductance in electron hydrodynamics

Linear temperature dependence of transport coefficients in metals is habitually viewed as a signature of non-Fermi-liquid physics, whereas the hallmark of Fermi-liquid physics is a T² scaling. in contrast to this comon lore, this talk will argue that two-dimensional electron fluids with simple Fermi surfaces feature conductivity that scales linearly with temperature. The T-linear scaling originates from nonclassical hydrodynamics in 2D Fermi systems governed by long-lived excitations and non-Newtonian viscous modes with scale-dependent viscosity. This behavior stands in sharp contrast with the conventional Gurzhi hydrodynamics in 3D systems that features a T² scaling of conductivity. The linear T dependence, predicted to occur in a wide range of temperatures, provides a smoking gun for nonclassical hydrodynamics. These findings explain the linear T dependence of conductance recently measured in 2D electron fluids.