Electron injection in a nanotube with leads: finite frequency noise-correlations and anomalous charges

TL;DR

This paper investigates how finite frequency noise correlations in a nanotube with leads reveal the anomalous charges of chiral excitations, overcoming zero-frequency limitations by analyzing spectral density at finite frequencies.

Contribution

It demonstrates that finite frequency noise spectra can uncover anomalous charges in nanotubes with leads, extending previous zero-frequency results for infinite systems.

Findings

Zero-frequency noise correlations vanish with leads.

Finite frequency noise spectra depend on quasiparticle travel time.

Spectral analysis allows extraction of anomalous charges.

Abstract

The non-equilibrium transport properties of a carbon nanotube which is connected to Fermi liquid leads, where electrons are injected in the bulk, are computed. A previous work which considered an infinite nanotube showed that the zero frequency noise correlations, measured at opposite ends of the nanotube, could be used to extract the anomalous charges of the chiral excitations which propagate in the nanotube. Here, the presence of the leads have the effect that such-noise cross-correlations vanish at zero frequency. Nevertheless, information concerning the anomalous charges can be recovered when considering the spectral density of noise correlations at finite frequencies, which is computed perturbatively in the tunneling amplitude. The spectrum of the noise cross-correlations is shown to depend crucially on the ratio of the time of flight of quasiparticles traveling in the nanotube to the ``voltage'' time which defines the width of the quasiparticle wave-packets injected when an electron tunnels. Potential applications toward the measurement of such anomalous charges in non-chiral Luttinger liquids (nanotubes or semiconductor quantum wires) are discussed.