Interaction induced dimerization in zigzag single wall carbon nanotubes

TL;DR

This paper develops a low-energy model for metallic zigzag carbon nanotubes, highlighting how interactions induce dimerization and can lead to quantum phase transitions affecting their electronic properties.

Contribution

It introduces a novel effective model that incorporates Coulomb interactions, umklapp scattering, and interaction-induced dimerization in zigzag nanotubes.

Findings

Interaction-induced dimerization can dominate the low-energy physics.

The ratio of dimerization gap to Mott gap depends on nanotube radius.

A quantum phase transition with SU(2)_1 symmetry can occur.

Abstract

We derive a low-energy effective model of metallic zigzag carbon nanotubes at half filling. We show that there are three important features characterizing the low-energy properties of these systems: the long-range Coulomb interaction, umklapp scattering and an explicit dimerization generated by interactions. The ratio of the dimerization induced gap and the Mott gap induced by the umklapp interactions is dependent on the radius of the nanotube and can drive the system through a quantum phase transition with SU(2)_1 quantum symmetry. We consider the physical properties of the phases on either side of this transition which should be relevant for realistic nanotubes.