《EPI on SMT》.pdf

Deduction for Effect of EPI on non-equilibrium transport through a SMT C.L Jin I. MODEL As shown in FIG.1, this model system is a single-electron level in a single-molecule transistor(SMT), which is coupled to the local vibration mode as well as to two metallic leads. To simplify the problem, we shall restrict ourselves exclusively to the effect of the electron-phonon interaction(EPI) and chemical potentials in two leads, ignoring other factors such as the intricacies of the real SMT, coulumb interaction, and spin effect. The model Hamiltonian can be expressed as = leads + ph + D + T , (1) where the first two terms is noninteracting electron gas in the leads and the local vibration mode of the SMT, respectively, ∑ † † = ϵ , = ω . (2) leads ph ∈LR Here ω is the local vibration frequency. The third term † † D = [ϵ + λ( + )] (3) describes the coupling between the SMT electron and the local phonon mode with strength λ. The last term T = ∑ [V† + h.c.] (4) ∈LR is hopping of the electron between the SMT and leads with the tunneling matrix elements denotes as V . In the strong EPI regime, it is appropriate to eliminate the EP coupling terms by using a nonperturba