Gate-dependent tunneling-induced level shifts observed in carbon nanotube quantum dots

We have studied electron transport in clean single-walled carbon nanotube quantum dots. Because of the large number of the Coulomb blockade diamonds simultaneously showing both shell structure and the Kondo effect, we are able to perform a detailed analysis of tunneling renormalization effects. Thus, determining the environment induced level shifts of this artificial atom. In shells where only one of the two orbitals is strongly coupled, we observe a marked asymmetric gate dependence of the inelastic cotunneling lines together with a systematic gate dependence of the size (and shape) of the Coulomb diamonds. These effects are all given a simple explanation in terms of second-order perturbation theory in the tunnel coupling.