Phonon emission and arrival times of electrons from a single-electron source

TL;DR

This paper investigates how hot electrons in quantum Hall edge channels relax via phonon emission, affecting their arrival times and explaining recent experimental observations of phonon-induced suppression and oscillations.

Contribution

It provides a theoretical analysis of phonon emission effects on electron relaxation and arrival times in quantum Hall edge channels, linking these to experimental results.

Findings

Phonon emission probability decreases double-exponentially with magnetic field.

Arrival-time distribution shows oscillations related to electron velocities after phonon emission.

Results explain recent experimental observations of electron relaxation in quantum Hall systems.

Abstract

In recent charge-pump experiments, single electrons are injected into quantum Hall edge channels at energies significantly above the Fermi level. We consider here the relaxation of these hot edge-channel electrons through longitudinal-optical phonon emission. Our results show that the probability for an electron in the outermost edge channel to emit one or more phonons en route to a detector some microns distant along the edge channel suffers a double-exponential suppression with increasing magnetic field. This explains recent experimental observations. We also describe how the shape of the arrival-time distribution of electrons at the detector reflects the velocities of the electronic states post phonon emission. We show how this can give rise to pronounced oscillations in the arrival-time-distribution width as a function of magnetic field or electron energy.