Electron-vibron coupling in suspended nanotubes

We consider the electron-vibron coupling in suspended nanotube quantum dots. Modelling the tube as an elastic medium, we study the possible coupling mechanism for exciting the stretching mode in a single-electron-transistor setup. Both the forces due to the longitudinal and the transverse fields are included. The effect of the longitudinal field is found to be too small to be seen in experiment. In contrast, the transverse field which couple to the stretching mode via the bending of the tube can in some cases give sizeable Franck-Condon factors. However, the length dependence is not compatible with recent experiments [Sapmaz et al. cond-mat/0508270].