Theory of the conductance of interacting quantum wires with good contacts and applications to carbon nanotubes

Abstract

Using bosonization we derive the dc conductance $G(L,T)$ of an interacting quantum wire with good contacts including current relaxing backscattering and umklapp processes. Our result yields the dependence of the conductance on length $L$ and temperature $T$ in the energy range where the Luttinger model is applicable. For a system where only a part of the current is protected by a conservation law, we surprisingly find an unreduced ideal quantum conductance as for a fully ballistic wire. As a second application, we calculate the conductance of metallic single-wall carbon nanotubes in an energy range where backscattering due to phonons dominates. In contrast to previous studies, we treat the electrons as interacting by using the Luttinger liquid formulation. The obtained results for the scaling of the dc conductance with temperature and length are compared with experimental data and yield a better description than the previously used noninteracting theory. Possible reasons for the remaining discrepancies in the temperature dependence between theory and experiment are discussed.