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

The current noise of a voltage biased interacting quantum wire adiabatically connected to metallic leads is computed in the presence of an impurity in the wire. This study aims to analyze the behavior of the Fano factor, which characterizes the ratio between noise and backscattered current, in relation to the noise frequency relative to the ballistic frequency. Findings indicate that in the weak backscattering limit, the Fano factor crucially depends on the frequency, revealing additional dependencies due to Andreev-type reflections at the contacts. Unlike chiral Luttinger liquids, the observed noise is influenced by both the Poissonian backscattering of fractionally charged quasiparticles and these Andreev reflections. This implies that careful analysis of frequency-dependent noise is necessary to extract the fractional charge of bulk excitations, specifically demonstrating how fractional quantum states can give rise to observed noise signatures in one-dimensional electronic systems. The implications of these results extend to the understanding of the statistics governing fractional charge excitations and their potential observational techniques in various experimental setups.