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

TL;DR

This paper develops a theoretical framework to analyze the full-counting statistics of energy transport in molecular junctions within the polaronic regime, revealing universal relations and transient behaviors of energy current cumulants.

Contribution

It introduces a novel formalism using Green's functions and Fredholm determinants to study energy transport dynamics and steady-state properties in the Anderson-Holstein model.

Findings

Universal relations for steady state energy current FCS derived

Transient energy current cumulants exhibit universal scaling

Numerical analysis of energy transport under temperature gradient and bias

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 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 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 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 in steady state under temperature gradient and external bias are numerically studied and explained. Transient dynamics of energy current cumulants is numerically calculated and analyzed. The universal scaling of normalized transient energy cumulants is found under both temperature gradient and external bias.