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.