Time-controlled charge injection in a quantum Hall fluid

TL;DR

This paper investigates controlled charge injection into fractional quantum Hall edge states, demonstrating that electronic correlations prevent divergence in charge fluctuations, contrasting with normal metal injection.

Contribution

It provides a perturbative and non-perturbative analysis of charge injection in fractional quantum Hall edge states using a Luttinger liquid model, highlighting the role of correlations.

Findings

Charge fluctuations are prevented from diverging due to correlations.

Explicit formulas for mean charge and fluctuations are derived.

Results are generalized to other Luttinger liquid systems like carbon nanotubes.

Abstract

We consider the injection of a controlled charge from a normal metal into an edge state of the fractional quantum Hall effect, with a time-dependent voltage $V(t)$. Using perturbative calculations in the tunneling limit, and a chiral Luttinger liquid model for the edge state, we show that the electronic correlations prevent the charge fluctuations to be divergent for a generic voltage pulse $V(t)$. This is in strong contrast with the case of charge injection in a normal metal, where this divergence is present. We show that explicit formul{ae} for the mean injected charge and its fluctuations can be obtained using an adiabatic approximation, and that non perturbative results can be obtained for injection in an edge state of the FQHE with filling factor $ nu=1/3$. Generalization to other correlated systems which can be described with the Luttinger liquid model, like metallic Carbon nanotube, is given.