Quantum Conductance of Interacting Quantum Wire By Current Relaxing Backscattering and Unklapp Processe

Abstract

We have studied the quantum conductance of interacting quantum wire by using current
relaxing back scattering and Umklap process. We have derived a general formula for the
conductance of interacting quantum wire with good contact and current relaxing processes in
the wire. We have shown that for an interacting ballistic wire contacted to leads were
generalized to an interacting wire with damping. We have calculated the resistance of an
interacting quantum wire which has coexisting ballistic and diffusive channels. Such
coexistence is expected for integrable modes where part of the current is protected by a local
or quasilocal conservation law. We have found that in such a case the ballistic channel is
small and completely dominates the transport so that the system shows ideal quantum
conductance. Relevant back scattering at the contact were found and were neglected. We
have calculated the resistance of single wall carbon nanotubes caused by a coupling to the
phononic degrees of freedom of the tube. Three modes have been taken into account. We
have found that there is damping of the phonons due to phonon-phonon interactions which
modified the phonon propagator. Backscattering is created by impurities which are often
relevant perturbations and completely suppress the conductance below a temperature scale.
Irrelevant backscattering due to phonons dominated in clean samples. Taking the electrons in
the carbon nanotubes as noninteracting it has been shown that acoustic phonon modes gave
rise to resistivity that increases linearly with temperature. The conductance showed thermally
activated behaviour. At every temperatures Umklapp scattering at half filling leaded to gaps
both in the charge and in the spin sector and thus to thermally activated behaviour. In a
device configuration the filling in the tube is usually tuned away from half filling so that the
Umklapp term oscillates. In the calculation the electrons are treated as noninteracting.
Calculation shows that one electron-electron interactions are included the interactions with
phonon modes of the tube alone give resistivity of the right magnitude even at room
temperature if standard parameters are used. The obtained results were found in good
agreement with previously obtained results