Quantum Conductance of Interacting Quantum Wire By Current Relaxing Backscattering and Unklapp Processes (Bulletin of Pure and Applied Sciences – Physics, 2021)
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.