Transport through a metallic carbon nanotube is considered, where electrons are injected in the bulk by a scanning tunneling microscope tip. The charge current and noise are computed both in the absence and in the presence of one dimensional Fermi liquid leads. For an infinite homogeneous nanotube, the shot noise exhibits effective charges different from the electron charge. Noise correlations between both ends of the nanotube are positive, and occur to second order only in the tunneling amplitude. The positive correlations are symptomatic of an entanglement phenomenon between quasiparticles moving right and left from the tip. This entanglement involves many body states of the boson operators which describe the collective excitations of the Luttinger liquid. I. INTRODUCTIONOver the years, the study of current noise and noise correlations has become a respected and useful diagnosis for transport measurements on mesoscopic conductors. Theoretically, noise was first computed mostly for non-interacting systems 1 . However, it soon became clear that low frequency noise could be used to isolate the quasiparticle charge 2,3 and to study the statistical correlations 4,5 in specific quasi one-dimensional correlated electron systems, such as the edge waves in the quantum Hall effect. In these chiral Luttinger liquids, the charge of the collective excitations along the edges corresponds to the electron charge multiplied by the filling factor.Attention is now turning towards conductors -individual nano-objects -which occur naturally, and which can be connected to current/voltage probes in order to perform a transport experiment. The crucial advantage of such nanoobjects is that they are essentially free of defects and in some circumstances they have an inherent one dimensional character. Carbon nanotubes constitute the archetype of such 1D nano-objects: single wall armchair nanotubes have metallic behavior, with two propagating modes at the Fermi level. Incidentally, electronic correlations are known to play an important role in such systems. Carbon nanotubes seem to constitute good candidates to study Luttinger liquid behavior. In particular, their tunneling density of states -and thus the tunneling I(V ) characteristics is known to have a power law behavior 6,7,8 in accordance with Luttinger liquid theory.Luttinger models for nanotubes differ significantly from their quantum Hall effect counterpart, because of their nonchiral character. Forward and backward fields describing collective excitations effectively mix, because the interactions between electrons are spread along the whole length of the nanotube. For this reason, a straightforward transposition of the results obtained for chiral edge system proves difficult. Nevertheless, non-chiral Luttinger liquids can be described with chiral fields 9,10 . Such chiral fields correspond to excitations with anomalous (non-integer) charge, which has eluded detection so far.In the present work, we propose an experimental geometry which allows to probe directly the underlying charg...

A fractional quantum Hall liquid with multiple edges is considered. The computation of transport quantities such as current, noise and noise cross correlations in such multiple edge samples requires the implementation of so called Klein factors, which insure the correct quasiparticle exchange properties. The commutation relations of these factors are obtained by closing the system into a single edge. The non-equilibrium Green's function formalism associated with such factors is derived for a simple Laughlin fraction of the Hall effect. It is shown explicitly how Klein factors enter the calculation of the noise cross correlations, as well as the correction to the Poisson limit for the noise.The edge state picture of the fractional quantum Hall effect [1] (FQHE) has led to fundamental discoveries. Various systems have been studied to analyze the quasiparticle excitations which tunnel through such quantum fluids [2,3]. In particular, for a point contact geometry with two edges, the detection of the backscattering noise leads to the measurement of the quasiparticle charge [4]. At the same time, resonant antidot tunneling geometries have allowed a capacitive measurement of the charge [5] in multiple edge geometries. Aside from this situation, multi edge geometries have not received much attention. Yet it was argued recently [6] that the detection of noise correlations in a three edge system constitutes a direct link to the quasiparticles statistics. One edge can be depleted due to the tunneling of quasiparticles into other edges. The Hanbury-Brown and Twiss type geometry [7] of Ref.[6] probes whether two quasi-holes on the injecting edge are allowed to overlap. Here, the key point is that quasiparticle edge tunneling operators need to be supplemented by Klein factors in order to specify the statistics. Klein factors were so far mostly introduced to tackle fermionic problems [8], yet it seems that their implementation is quite relevant for complex fractional Hall geometries.The purpose here is to give a pedagogical view of how fractional statistics enters these multiple edge geometries: which (fractional) phase is generated when two quasiparticles from different edges are exchanged ? We focus on Laughlin filling factors ν = (2p + 1) −1 (p integer). First, specifying a quasiparticle tunneling Hamiltonian, we derive the algebra which is obeyed by Klein factors. Next, we introduce the Keldysh Green's functions for the Klein factors. These tools are then applied to study the non-equilibrium current and noise correlations in a multi-edge system. In particular, it will be shown that Klein factors are unnecessary for simple, two edge samples. Finally, we argue that when considering the non-equilibrium average of a tunneling operator between two edges, there remains always a contribution associated with Klein factors, which is symptomatic of quasiparticle exchange with other edge "reservoirs".

The transport properties of a simple model for a finite level structure (a molecule or a dot) connected to metal electrodes in an alternating current scanning tunneling microscope (ac-STM) configuration is studied. The finite level structure is assumed to have strong binding properties with the metallic substrate, and the bias between the STM tip and the hybrid metal-molecule interface has both an ac and a dc component. The finite frequency current response and the zero-frequency photoassisted shot noise are computed using the Keldysh technique, and examples for a single-site molecule (a quantum dot) and for a two-site molecule are examined. The model may be useful for the interpretation of recent experiments using an ac-STM for the study of both conducting and insulating surfaces, where the third harmonic component of the current is measured. The zero-frequency photoassisted shot noise serves as a useful diagnosis for analyzing the energy level structure of the molecule. The present work motivates the need for further analysis of current fluctuations in electronic molecular transport.