Electronic wave-packets in integer quantum Hall edge channels: relaxation and dissipative effects

TL;DR

This paper models the evolution of electronic wave-packets in quantum Hall edge channels, highlighting the importance of dissipation effects and matching theoretical predictions with experimental data.

Contribution

It introduces a theoretical framework incorporating dissipation effects to explain wave-packet relaxation in quantum Hall edge channels, aligning with recent experiments.

Findings

Linear energy loss best fits experimental data

Quadratic dissipation dependence is ruled out

Non-dissipative models do not match observations

Abstract

We theoretically investigate the evolution of the peak height of an energy resolved electronic wave-packets ballistically propagating along integer quantum Hall edge channels at filling factor $\nu=2$. This is ultimately related to the elastic scattering amplitude for the fermionic excitations evaluated at different injection energy. We investigate this quantity assuming a short range capacitive coupling between the edges. Moreover, we also take into account phenomenologically the possibility of energy dissipation towards additional degrees of freedom both linear and quadratic in the injection energy. Comparing with recent experimental data, we rule out the non-dissipative case as well a quadratic dependence of the dissipation, indicating a linear energy loss rate as the best candidate to describe the behavior of the quasi-particle peak at short enough propagation lengths.