Theory of the Conductivity in Semiconducting Single-Wall Carbon Nanotubes

TL;DR

This paper develops a theoretical framework explaining how the conduction properties of single-wall carbon nanotubes depend on their geometric structure, distinguishing between semiconducting and metallic behaviors, and explores low-temperature conduction mechanisms.

Contribution

It provides a theoretical model linking nanotube geometry to conduction type and introduces phonon-mediated Cooper pairing as a conduction mechanism at low temperatures.

Findings

Semiconducting behavior occurs when the pitch includes an integral number of hexagons.

Metallic behavior arises otherwise, with conduction in the graphene wall.

Low-temperature conduction is dominated by phonon-mediated Cooper pairs.

Abstract

The conduction of a single-wall carbon nanotube depends on the pitch. If there are an integral number of carbon hexagons per pitch, then the system is periodic along the tube axis and allows "holes" (, and not "electrons",) to move inside the tube. This case accounts for a semiconducting behavior with the activation energy of the order of around 3 meV. There is a distribution of the activation energy since the pitch and the circumference can vary. Otherwise nanotubes show metallic behaviors. "Electrons" and "holes" can move in the graphene wall (two dimensions). The conduction in the wall is the same as in graphene if the finiteness of the circumference is disregarded. Cooper pairs formed by the phonon exchange attraction moving in the wall is shown to generate a temperature-independent conduction at low temperature (3-20 K).