Electron-vibron coupling in suspended carbon nanotube quantum dots

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 exhibit vibrational sidebands accompanied by the Franck-Condon blockade with strong electron-vibron coupling.

Figure 1

Schematic description of the acoustic phonon modes of CNT. (a) Unperturbed nanotube. (b) Stretching mode. (c) Breathing mode. (d) Twist mode. (e) Bending mode with $n=1$ at finite $q$. (f) Bending mode with $n=2$ and $q=0$.

Figure 2

Schematic description of the electronic quantum dot of size $L_d$ (in gray) along a carbon nanotube of length $L$.

Figure 3

Schematic description of the electron confinement producing quantum dots in semiconducting (a) and metallic (b) carbon nanotubes. Here $y_0=0$.