Phonon-assisted shot noise through a quantum dot weakly coupled to Luttinger liquid

In the present paper, by applying the Lang–Firsov canonical transformation and the nonequilibrium Green function technique, we investigate joint effects of the electron–phonon interaction and intralead electron interaction on the differential shot noise and Fano factor through a vibrating quantum dot weakly coupled to Luttinger liquid leads. The influences of electron–phonon coupling and intralead electron interaction on differential shot noise and Fano factor are studied in detail. Variation of the main resonant peak and phonon satellite peaks with the electron–phonon interaction and electron–electron interaction of the leads is analyzed numerically. Besides, we also reproduced the result for the differential conductance derived by Skorobagat’ko and Krive using the master equation.