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

Vincent F. Kershaw, Daniel S. Kosov

Published 2020-07-31Version 1

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. Conversely, the current-driven nuclear dynamics feed back to the electronic current, which can be captured according extended formula for the current that has an explicit dependency on classical nuclear velocities and accelerations. Current-induced nuclear forces and the non-adiabatic electric currents 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 conductivities. 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 current noise are explored for an effective adiabatic potential morphs between a single, double and triple potential as a function of voltage.