Local Franck-Condon factors in suspended carbon nanotube quantum dots

We investigate the effects of the coupling between quantized vibrational modes (vibrons) and electronic degrees of freedom in suspended carbon nanotube quantum dots. The elastic deformations couple both to the total dot charge and to its spatial density fluctuations. The latter, neglected in the Anderson-Holstein model, have profound consequences if the size of the vibron and of the dot do not coincide, as is generically the case in experimental devices. When the vibron is smaller than the quantum dot, spatially varying local Franck-Condon factors emerge with striking effects on the transport properties of the system. The theoretical results are supported by our experimental observations.