Phonon-assisted tunneling and two-channel Kondo effect in a vibrating molecular dot coupled to Luttinger liquid leads

• Phonon-assisted Green's function in the Kondo regime is deprived.
• A single-molecular quantum dot weakly coupled to Luttinger liquid leads.
• The electron–phonon interaction yields satellite peaks around the Kondo peak.
• Intralead electron interaction turns the Kondo and satellite peaks gradually into dips.

We study the joint effects of the electron–phonon interaction (EPI) and intralead electron interaction (IEI) on the density of states (DOS) of a single-molecular quantum dot weakly coupled to Luttinger liquid leads in the Kondo regime by using the extended non-equilibrium Green's function method. The introduction of the EPI yields satellite peaks around the Kondo peak. With the increase of the IEI, all the peak heights reduce and then turn to dips. The full crossover in the DOS from the phonon-assisted one-channel physics to two-channel physics is exhibited. The inelastic tunneling will dominate electron transport for a certain region of interaction strength.