Electron injection in a nanotube with leads: Finite-frequency noise correlations and 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 crosscorrelations 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 crosscorrelations 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.

Charge and spin fractionalization beyond the Luttinger-liquid paradigm

“…Experimental evidences of its existence have been observed in quasi-1D organic conductors 3 , semiconductor quantum wires 4 , and quantum chains on semiconductor surfaces 5 . The LL theory also predicts the fractionalization of injected charge into two chiral modes (leftand right-going) [6][7][8][9][10] , a phenomenon recently confirmed experimentally 11 . Along the experimental advances also theoretical progress was recently achieved pertaining extensions beyond the LL limit by incorporating nonlinearity of the dispersion, leading to qualitative changes in the spectral function [12][13][14][15][16] and relaxation processes of 1D electronic systems 17 .…”

Measuring Noise and Cross Correlations at High Frequencies in Nanophysics

“…This promises to have applications in the detection of fractional charges in carbon nanotubes 12 as well as in the detection of electronic entanglement 18 . For capacitive coupling to an NS circuit, by controlling the detector circuit (varying eV and ǫ D ), we can make a mapping of the spectral density of noise.…”

“…Low frequency noise cross-correlations measurements have also been performed 9,10 , which showed that a fully degenerate electron gas has negative noise correlations. Yet, finite frequency noise cross-correlations are useful in the study of electronic entanglement in mesoscopic devices 11 , and in the identification of anomalous charges in Luttinger liquid wires 12 . The purpose of the present paper is twofold: to suggest a way to measure noise cross-correlation with inductive coupling, and to suggest a way to measure noise via photo-assisted Andreev reflection in a capacitive coupling setup.…”

Charge fractionalization in nonchiral Luttinger systems

“…Point-like tunneling would not be judicious to probe charge fractionalization since it results in I − S = I + S = I S /2; see Appendix B.1. It should also be mentioned that the effective charges in the shot-noise formula (21) and (22) are extremally sensitive to the couplings with measuring leads [23,24,25], i.e., the anomalous charges are difficult to observe through shot-noise measurements at low frequency.…”