Frictional drag between quantum wells mediated by phonon exchange

TL;DR

This paper investigates the frictional drag between quantum wells mediated by phonon exchange, revealing how phonon scattering and collective modes influence the drag rate, and aligns well with experimental data.

Contribution

It introduces a theoretical framework incorporating phonon scattering effects and electron-phonon collective modes to explain drag phenomena in quantum wells.

Findings

Drag rate diverges with free phonons but becomes finite with scattering.

Imperfection scattering causes drag rate to vary as ln(ell_ph/d).

Electron-phonon collective modes dominate at large phonon mean free paths.

Abstract

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.