Nonequilibrium Green's function theory for nonadiabatic effects in quantum electron transport

TL;DR

This paper introduces a nonequilibrium Green's function framework that incorporates nonadiabatic nuclear motion effects into quantum electron transport calculations, providing analytic expressions and extended current formulas.

Contribution

It develops a perturbative approach using Wigner representation to include nonadiabatic effects in Green's functions for molecular junctions, advancing transport theory.

Findings

Derived analytic expressions for nonadiabatic Green's functions up to second order.

Extended current formula accounting for nuclear velocities and accelerations.

Validated the theory with model molecular junction calculations.

Abstract

We develop nonequilibribrium Green's function based transport theory, which includes effects of nonadiabatic nuclear motion in the calculation of the electric current in molecular junctions. Our approach is based on the separation of slow and fast timescales in the equations of motion for the Green's functions by means of the Wigner representation. Time derivatives with respect to central time serves as a small parameter in the perturbative expansion enabling the computation of nonadiabatic corrections to molecular Green's functions. Consequently, we produce series of analytic expressions for non-adiabatic electronic Green's functions (up to the second order in the central time derivatives); which depend not solely on instantaneous molecular geometry but likewise on nuclear velocities and accelerations. Extended formula for electric current is derived which accounts for the non-adiabatic corrections. This theory is concisely illustrated by the calculations on a model molecular junction.