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

Frictional drag between quantum wells mediated by phonon exchange