Full-counting statistics of energy transport of molecular junctions in the polaronic regime

Abstract

We investigate the full-counting statistics (FCS) of energy transport carried by electrons in molecular junctions for the Anderson-Holstein model in the polaronic regime. Using the two-time quantum measurement scheme, the generating function (GF) for the energy transport is derived and expressed as a Fredholm determinant in terms of Keldysh nonequilibrium Green's function in the time domain. Dressed tunneling approximation is used in decoupling the phonon cloud operator in the polaronic regime. This formalism enables us to analyze the time evolution of energy transport dynamics after a sudden switch-on of the coupling between the dot and the leads towards the stationary state. The steady state energy current cumulant GF in the long time limit is obtained in the energy domain as well. Universal relations for steady state energy current FCS are derived under a finite temperature gradient with zero bias and this enabled us to express the equilibrium energy current cumulant by a linear combination of lower order cumulants. The behaviors of energy current cumulants in steady state under temperature gradient and external bias are numerically studied and explained. The transient dynamics of energy current cumulants is numerically calculated and analyzed. Universal scaling of normalized transient energy cumulants is found under both temperature gradient and external bias.where 0  is the bare electronic energy level, and 0 w is the frequency of the localized vibron. d † (a † ) denotes the electron (phonon) creation operator in the QD. The localized vibron modulates the QD with the electronphonon coupling constant t ep . The Hamiltonians of the leads is given in a compact form

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