Probing interactions via non-equilibrium momentum distribution and noise in integer quantum Hall systems at $\nu=2$

TL;DR

This paper investigates how electron-electron interactions in integer quantum Hall edge channels at filling factor 2 lead to fractional excitations, analyzing their structure via non-equilibrium momentum distributions and noise measurements, especially under Lorentzian drives.

Contribution

It introduces a method to analyze fractional excitations and their interactions through non-equilibrium momentum distributions and noise, providing a way to measure inter-channel interactions in quantum Hall systems.

Findings

Fractional excitations emerge due to electron-electron interactions.

Zero frequency noise can be used to probe inter-channel interactions.

Lorentzian drives produce minimal excitations known as Levitons.

Abstract

We consider the excitation of single-electron wave packets by means of a time dependent voltage applied to the ballistic edge channels of the integer quantum Hall effect at filling factor $\nu=2$. Due to electron-electron interactions, fractional excitations emerge along the edge. Their detailed structure is analyzed by evaluating the nonequilibrium momentum distributions associated with the different edge channels. We provide results for a generic time-dependent drive both in the stationary regime and for intermediate times, where the overlap between fractionalized wave packets carries relevant information on interaction strength. As a particular example we focus on a Lorentzian drive, which provides a clear signature of the minimal excitations known as Levitons. Here, we argue that inner-channel fractionalized excitations can be exploited to extract information about inter-channel interactions. We further confirm this idea by calculating the zero frequency noise due to the partitioning of these excitations at a quantum point contact and we propose a measurable quantity as a tool to directly probe electron-electron interactions and determine the so-called mixing angle of copropagating quantum Hall channels.