Quantum Interactions in nanostructures

When current flows in an electrical conductor, it exerts forces on the atoms, much like a river pushes rocks in its way. In nanoscale conductors, the current densities attainable under experimentally accessible conditions can exceed those in macroscopic conductors by many orders of magnitude. As a consequence, current-induced forces on atoms in nanowires can be very large. We have shown in the past that these forces are non-conservative, meaning that they can do net work on atoms around closed paths. This property generates a new energy-transfer mechanism from the current into the atomic motion. This opens up the possibility of exploiting these forces to serve as the drivers of atomic-scale engines. At the same time, it constitutes an additional - and potentially powerful - failure mechanism for these tiny systems, over and above the effects of Joule heating. Understanding these forces - and how large or small they are - is therefore of paramount importance for the functionality of nanoscale devices.

This is a very hard problem because it combines the need to describe the interactions between the non-equilibrium current-carrying electrons and the nuclei in the system with an account of other interactions, such as - importantly - those between electrons and other electrons. In physical terms, electron-electron screening determines how electrons behave in the vicinity of the scattering centres and may thus be expected to affect the resultant current-induced forces. In all our past work on this problem - extending over more than ten years now - we have taken a mean-field view of electron-electron interactions and have often worked with non-interacting electrons altogether. This has been a price worth paying in order to obtain a tractable problem, open to non-equilibrium molecular dynamics simulations. We have shown however that - at mean-field level - electron-electron screening can substantially reduce non-conservative current-induced forces. Thus, the effect of screening on the forces is potentially far from trivial. It is now time to consider this problem beyond the mean-field picture, in order to establish the effect of electron-electron interactions on this crucially important effect. This is the aim of the present project.

Our initial line of approach to the problem is as follows. In the past we have derived an expression for a quantity that directly quantifies the degree of non-conservativeness of current-induced forces. This quantity is a generalized curl. Our expression is based on a mean-field treatment of electron-electron interactions, as highlighted above. The aim now becomes to investigate the corrections to this expression introduced by electron correlation. Our initial choice of framework, in which to study the problem, is non-equilibrium Green's function theory. This choice is dictated by the fact that mean-field result above was obtained within this framework.

Here however we come upon another key aspect of the project. This is not work in isolation. There has been a growing effort in the vibrant international community interested in non-equilibrium electron-nuclear dynamics in the question at the heart of our project: how do electron-electron interactions affect electron-nuclear interactions? From the very beginning we have sought to embed our work in this dynamical and ever-expanding context. We have been in touch with colleagues from two leading groups where there is such an effort underway. The aim is to initiate a discussion on the most promising avenues towards the shared goal. We furthermore have long-standing links with other leading researchers in the field, including both theory and experiment, with a specific emphasis on non-conservative forces and current-driven atomic motion in nanoscale junctions. These new and existing contacts will provide a helpful setting for our forthcoming work, with a pronounced international dimension.