Electron-vibron coupling in suspended carbon nanotube quantum dots

TL;DR

This paper investigates how different vibrational modes in suspended carbon nanotube quantum dots interact with electrons, revealing mode-dependent coupling strengths that explain experimental vibrational sidebands and Franck-Condon blockade phenomena.

Contribution

It provides a detailed analysis of mode-specific electron-vibron coupling mechanisms in carbon nanotubes, highlighting the dependence on inhomogeneity and mode symmetry.

Findings

Longitudinal and radial modes have strong coupling via deformation potential.

Twist modes couple weakly through hopping modulation.

Bending modes exhibit quadratic coupling due to symmetry.

Abstract

Motivated by recent experiments, we investigate the electron-vibron coupling in suspended carbon nanotube quantum dots, starting with the electron-phonon coupling of the underlying graphene layer. We show that the coupling strength depends sensitively on the type of vibron and is strongly sample dependent. The coupling strength becomes particularly strong when inhomogeneity-induced electronic quantum dots are located near regions where the vibronic mode is associated with large strain. Specifically, we find that the longitudinal stretching mode and the radial breathing mode are coupled via the strong deformation potential, while twist modes couple more weakly via a mechanism involving modulation of the electronic hopping amplitudes between carbon sites. A special case are bending modes: for symmetry reasons, their coupling is only quadratic in the vibron coordinate. Our results can explain recent experiments on suspended carbon nanotube quantum dots which exibit vibrational sidebands accompanied by the Franck-Condon blockade with strong electron-vibron coupling.