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

TL;DR

This paper derives the conductance behavior of interacting quantum wires, including carbon nanotubes, considering interactions and scattering processes, and compares theoretical predictions with experimental data.

Contribution

It provides a novel theoretical framework using bosonization to analyze conductance in interacting quantum wires with realistic contacts.

Findings

Conductance depends on length and temperature within the Luttinger model range.

Interacting electrons can preserve ideal conductance despite partial current protection.

The theory aligns better with experimental data than non-interacting models.

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 non-interacting theory. Possible reasons for the remaining discrepancies in the temperature dependence between theory and experiment are discussed.