Appearance of fractional charge in the noise of non-chiral Luttinger liquids

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 noise and backscattered current crucially depends on the noise frequency $\omega$ 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 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.