# Hydrodynamic Coulomb drag and bounds on diffusion

## TL;DR

This paper investigates Coulomb drag in a two-layer electron system, revealing a temperature regime where hydrodynamic effects dominate and connect resistivity to electron-electron scattering rates, supporting Planckian dissipation.

## Contribution

It identifies an intermediate temperature regime where hydrodynamic Coulomb drag resistivity is proportional to electron-electron scattering rate, linking it to Planckian relaxation times.

## Key findings

- Hydrodynamic drag resistivity scales with electron-electron scattering rate.
- Proposes a temperature range where resistivity reflects fast electron-electron interactions.
- Supports the idea that linear resistivity can originate from Planckian dissipation.

## 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.