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

Gaomin Tang, Zhizhou Yu, Jian Wang

Published 2016-12-09Version 1

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 two-time quantum measurement scheme, 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 facilitates 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. Transient dynamics of energy current cumulants is numerically calculated and analyzed. The universal scaling of normalized transient energy cumulants is found under both the temperature gradient and external bias. 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 is derived under finite temperature gradient with zero bias and this enables us to express the equilibrium energy current cumulant by a linear combination of lower order cumulants. Behaviors of energy current cumulants under temperature gradient and external bias are numerically shown and explained.