Influence of electron-phonon coupling on low temperature phases of metallic single-wall carbon nanotubes

TL;DR

This study explores how electron-phonon interactions influence low-temperature phases in metallic single-wall carbon nanotubes, revealing phase diagram differences between armchair and zigzag types through a renormalization group approach.

Contribution

It introduces a two-cutoff scaling scheme to analyze electron-phonon effects, showing phonon softening and Peierls insulator formation in armchair nanotubes, unlike zigzag nanotubes.

Findings

Phonon softening occurs in armchair nanotubes with strong electron-phonon coupling.

Peierls insulator phase emerges in armchair nanotubes due to phonon softening.

Electron-phonon effects are negligible in zigzag nanotubes.

Abstract

We investigate the effect of electron-phonon coupling on low temperature phases in metallic single-wall carbon nanotubes. We obtain low-temperature phase diagrams of armchair and zigzag type nanotubes with screened interactions with a weak-coupling renormalization group approach. In the absence of electron-phonon coupling, two types of nanotubes have similar phase diagrams. A $D$-Mott phase or $d$-wave superconductivity appears when the on-site interaction is dominant, while a charge-density wave or an excitonic insulator phase emerges when the nearest neighbor interaction becomes comparable to the on-site interaction. The electron-phonon coupling, treated by a two-cutoff scaling scheme, leads to different behavior in two types of nanotubes. For strong electron-phonon interactions, phonon softening is induced and a Peierls insulator phase appears in armchair nanotubes. We find that this softening of phonons may occur for any intraband scattering phonon mode. On the other hand, the effect of electron-phonon coupling is negligible for zigzag nanotubes. The distinct behavior of armchair and zigzag nanotubes against lattice distortion is explained by analysis of the renormalization group equations.