Frictional drag between quantum wells mediated by phonon exchange

We use the Kubo formalism to evaluate the contribution of acoustic phonon exchange to the frictional drag between nearby two-dimensional electron systems. In the case of free phonons, we find a divergent drag rate ($\tau_{D}^{-1}$). However, $\tau_{D}^{-1}$ becomes finite when phonon scattering from either lattice imperfections or electronic excitations is accounted for. In the case of GaAs quantum wells, we find that for a phonon mean free path $\ell_{ph}$ smaller than a critical value, imperfection scattering dominates and the drag rate varies as $ln (\ell_{ph}/d)$ over many orders of magnitude of the layer separation $d$. When $\ell_{ph}$ exceeds the critical value, the drag rate is dominated by coupling through an electron-phonon collective mode localized in the vicinity of the electron layers. We argue that the coupled electron-phonon mode may be observable for realistic parameters. Our theory is in good agreement with experimental results for the temperature, density, and $d$-dependence of the drag rate.