Fractional charge in the noise of Luttinger liquid systems

TL;DR

This paper investigates how current noise in an interacting quantum wire reveals fractional charge, showing that frequency-dependent noise analysis can uncover interaction effects and fractional quasiparticles.

Contribution

It demonstrates that the frequency dependence of shot noise in a Luttinger liquid wire reveals fractional charge and interaction effects, considering contact reflections and impurity backscattering.

Findings

Fano factor depends on noise frequency relative to ballistic frequency

Noise reveals fractional charge e* = e g in the bulk excitations

Interaction effects are observable within experimental frequency ranges

Abstract

The current noise of a voltage biased interacting quantum wire adiabatically connected to metallic leads is computed in presence of an impurity in the wire. We find that in the weak backscattering limit the Fano factor characterizing the ratio between shot noise and backscattering current crucially depends on the noise frequency relative to the ballistic frequency v_F/gL, where v_F is the Fermi velocity, g the Luttinger liquid interaction parameter, and L the length of the wire. In contrast to chiral Luttinger liquids, the noise is not only due to the Poissonian backscattering of fractionally charged quasiparticles at the impurity, but also depends on Andreev-type reflections of plasmons at the contacts, so that the frequency dependence of the noise needs to be analyzed to extract the fractional charge e*=e g of the bulk excitations. We show that the frequencies needed to see interaction effects in the Fano factor are within experimental reach.