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

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.

arXiv comment17 pages and 8 figures

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• A semiclassical nonequilibrium Green's Function approach to electron transport in systems exhibiting electron-phonon couplings