Electron-phonon correlation effects in molecular transistors

The interplay of electron-electron and electron-phonon interactions is studied analytically in the Kondo regime. A Holstein electron-phonon coupling is shown to produce a weakening of the gate voltage dependence of the Kondo temperature and may explain the observed anomalies in some of these devices. A molecular center-of-mass mode opens a new channel for charge and spin fluctuations and in the antiadabatic limit the latter are described by an asymmetric two-channel Kondo model. Below the Kondo temperature the system develops a dynamical Jahn-Teller distortion and a low energy peak emerges in the phonon spectral density that could be observed in Raman microscopy experiments.