Energy relaxation in hot electron quantum optics via acoustic and optical phonon emission

TL;DR

This paper models the energy relaxation of hot electrons in quantum Hall edge channels through acoustic and optical phonon emission, providing insights into electron energy distributions and emission rates relevant to single-electron experiments.

Contribution

It introduces a comprehensive theoretical model that combines phonon emission processes and derives an effective drift-diffusion description for electron energy relaxation.

Findings

Effective optical phonon emission rate including inter-edge-channel transitions

Energy loss and broadening due to acoustic phonons characterized

Simulation results align with experimental observations of electron relaxation

Abstract

We study theoretically the relaxation of hot quantum-Hall edge-channel electrons under the emission of both acoustic and optical phonons. Aiming to model recent experiments with single-electron sources, we describe simulations that provide the distribution of electron energies and arrival times at a detector a fixed distance from the source. From these simulations we extract an effective rate of emission of optical phonons that contains contributions from both a direct emission process as well as one involving inter-edge-channel transitions that are driven by the sequential emission of first an acoustic -- and then an optical -- phonon. Furthermore, we consider the mean energy loss due to acoustic phonon emission and resultant broadening of the electron energy distribution and derive an effective drift-diffusion model for this process.