Theory of Current and Shot Noise Spectroscopy in Single-Molecular   Quantum Dots with Phonon Mode
  Using the Keldysh nonequilibrium Green function technique, we study the current and shot noise spectroscopy of a single molecular quantum dot coupled to a local phonon mode. It is found that in the presence of electron-phonon coupling, in addition to the resonant peak associated with the single level of the dot, satellite peaks with the separation set by the frequency of phonon mode appear in the differential conductance. In the ``single level'' resonant tunneling region, the differential shot noise power exhibit two split peaks. However, only single peaks show up in the ``phonon assisted'' resonant-tunneling region. An experimental setup to test these predictions is also proposed. 
Jian-Xin Zhu and A. V. Balatsky