Non-Adiabatic Effects of Nuclear Motion in Quantum Transport of Electrons: A Self-Consistent Keldysh-Langevin Study

TL;DR

This paper develops a self-consistent quantum transport model incorporating non-adiabatic nuclear motion effects in molecular junctions, revealing significant differences from equilibrium models and highlighting phenomena like the Landauer blowtorch effect.

Contribution

It introduces a novel theoretical framework combining non-equilibrium Green's functions with nuclear dynamics, capturing non-adiabatic effects in quantum transport.

Findings

Non-adiabatic corrections significantly affect current characteristics.

Non-equilibrium nuclear motion leads to higher conductance profiles.

The Landauer blowtorch effect influences current and noise properties.

Abstract

The molecular junction geometry is modelled in terms of nuclear degrees of freedom that are embedded in a stochastic quantum environment of non-equilibrium electrons. Time-evolution of the molecular geometry is governed via a mean force, a frictional force and a stochastic force, forces arising from many electrons tunnelling across the junction for a given nuclear vibration. Conversely, the current-driven nuclear dynamics feed back to the electronic current, which can be captured according extended expressions for the current that have explicit dependencies on classical nuclear velocities and accelerations. Current-induced nuclear forces and the non-adiabatic electric current are computed using non-equilibrium Green's functions via a time-scale separation solution of Keldysh-Kadanoff-Baym equations in Wigner space. Applying the theory to molecular junctions demonstrated that non-adiabatic corrections play an important role when nuclear motion is considered non-equilibrium and, in particular, showed that non-equilibrium and equilibrium descriptions of nuclear motion produce significantly different current characteristics. It is observed that non-equilibrium descriptions generally produce heightened conductance profiles relative to the equilibrium descriptions and provide evidence that the effective temperature is an effective measure of the steady-state characteristics. Finally, we observe that non-equilibrium descriptions of nuclear motion can give rise to the Landauer blowtorch effect via the emergence of multi-minima potential energy surfaces in conjunction with non-uniform temperature profiles. The Landauer blowtorch effect and its impact on the current characteristics, waiting times and the Fano factor are explored for an effective adiabatic potential that morphs between a single, double and triple potential as a function of voltage.