Piezoelectric electron-phonon interaction in impure semiconductors: 2D electrons versus composite fermions

TL;DR

This paper develops a unified theory of piezoelectric electron-phonon interactions in 2D electron systems, including effects of impurities and magnetic fields, with applications to GaAs/AlGaAs heterostructures.

Contribution

It introduces a comprehensive framework for electron-phonon coupling in 2D systems under magnetic fields, accounting for impurity effects and contrasting with deformation potential interactions.

Findings

Impurity-renormalized electron-phonon vertices do not cancel out as in deformation potential cases.

Calculated electron energy relaxation times and phonon emission rates for GaAs/AlGaAs heterostructures.

Analyzed differences between zero and strong magnetic field regimes in electron-phonon interactions.

Abstract

We develop a unified treatment of the piesoelectric coupling between two-dimensional electrons and bulk phonons in both cases of zero and strong magnetic fields, the latter corresponding to even denominator filling fractions. In contrast to the case of coupling via the deformation potential, the leading contributions due to impurity-renormalized electron-phonon vertices are not exactly cancelled by processes of inelastic electron-impurity scattering. Electron energy relaxation time, diffusion correction to the conductivity, and phonon emission rate by hot electrons are computed for realistic $GaAs/AlGaAs$ heterostructures.