Effects of decoherence on the shot noise in carbon nanotubes

We study the zero frequency noise in an interacting quantum wire connected to leads, in the presence of an impurity. In the absence of quasiparticle decoherence the zerofrequency noise is that of a non-interacting wire. However, if the collective, fractionallycharged modes have a finite lifetime, we find that the zero-frequency noise may still exhibit signatures of charge fractionalization, such as a small but detectable reduction of the ratio between the noise and the backscattered current (Fano factor). We argue that this small reduction of the Fano factor is consistent with recent observations of a large reduction in the experimentally-inferred Fano factor in nanotubes (calculated assuming that the backscattered current is the difference between the ideal current in a multiple-channel non-interacting wire and the measured current). Shot noise has been long used to extract information about the nature of the elementary excitations in a system. Thus, shot noise measurements have been used extensively to study exotic phases, such as the ones arising in strongly interacting one-dimensional systems. For example they confirmed the presence of fractionally charged quasiparticles in a fractional quantum Hall fluid [1]. While various proposals have been made to use shot noise to characterize other one-dimensional systems such as carbon nanotubes [2, 3, 4, 5, 6], a clear confirmation of the fractionalized nature of the elementary quasiparticles in nanotubes is still lacking. The major effect that obscures the fractional character of the excitations in nanotubes (and other nonchiral one-dimensional systems) is the presence of metallic leads: at small frequencies the noise probes the physics of the non-interacting leads, and not the physics of the nanotube. Thus, while in a chiral Luttinger liquid (LL) (such as a fractional quantum Hall effect (FQHE) edge state system), the Fano factor, defined as the ratio betwen the noise and the backscattered current, is equal to the fractional charge ge, in a nanotube the Fano factor has been predicted [3] to be simply equal to the electron charge e. Recent experiments [7, 8] have measured the Fano factor in nanotubes, and observed nevertheless a reduced Fano factor. The value of the observed Fano factor in Ref. [7] is roughly 0.4e – too small to be explained by the non-interacting physics of the leads [3], but also too large to be consistent with the presumed value of the fractional charge in nanotubes (0.2e) [2].