Hydrodynamic Coulomb drag and bounds on diffusion

Abstract

We study Coulomb drag between an active layer with a clean electron liquid and a passive layer with a pinned electron lattice in the regime of fast intralayer equilibration. Such a two-fluid system offers an experimentally realizable way to disentangle the fast rate of intralayer electron-electron interactions from the much slower rate of momentum transfer between both layers. We identify an intermediate temperature range above the Fermi energy of the electron fluid but below the Debye energy of the electronic crystal where the hydrodynamic drag resistivity is directly proportional to a fast electron-electron scattering rate. The results are compatible with the conjectured scenario for strong electron-electron interactions which poses that a linear temperature dependence of resistivity originates from a "Planckian" electron relaxation time $\tau_{eq}\sim \hbar/k_BT$. We compare this to the better known semiclassical case, where the diffusion constant is found to be not proportional to the microscopic timescale.