Charge Fractionalization on Quantum Hall Edges

TL;DR

This paper explores how localized charges propagate and fractionalize on quantum Hall edges, revealing the formation of fractional charges and proposing methods for their experimental detection through noise measurements.

Contribution

It introduces a detailed analysis of charge fractionalization in quantum Hall edges with variable widths, highlighting the role of Luttinger liquid interactions and numerical simulations.

Findings

Charge pulses split into a sharp front and a broad tail.

The front pulse carries a fractional charge of rac12;g times the electron charge.

Fractional charges can be detected via noise measurements in tunneling experiments.

Abstract

We discuss the propagation and fractionalization of localized charges on the edges of quantum Hall bars of variable widths, where interactions between the edges give rise to Luttinger liquid behavior with a non-trivial interaction parameter g. We focus in particular on the separation of an initial charge pulse into a sharply defined front charge and a broader tail. The front pulse describes an adiabatically dressed electron which carries a non-integer charge, which is \sqrt{g} times the electron charge. We discuss how the presence of this fractional charge can, in principle, be detected through measurements of the noise in the current created by tunneling of electrons into the system. The results are illustrated by numerical simulations of a simplified model of the Hall bar.