Electrons and nuclei in tiny wires

We can see and feel - and even hear and smell - what current flow can do in lightbulbs. They heat up, emit light, and eventually burn out. So how about the thinnest wires possible in nature, such as chains of single atoms and molecular junctions, which can be produced experimentally with high degrees of control? The difference is not just size. The current densities (current per unit cross-sectional area) in atomic wires can exceed those in a lightbulb filament by many orders of magnitude. How the electrons and the nuclei behave under these conditions is an open question, to both experiment and theory.

For many years our group has worked on the question of how current flow in these systems affects the dynamics of the atomic nuclei. A lot has been achieved and learned about these conducting systems, and a range of methodologies exists, proposed by research groups worldwide, depending on the questions to address.

Effects familiar from everyday experience occur at the atomic scale too. For example, Joule heating can take place in atomic wires and can result in a large local temperature rise. Another exciting development was our demonstration that current can exert an additional, non-conservative force field on atoms, with the possibility of using current as the driver for atomic-scale engines, by analogy with how a stream can drive a waterwheel. At the same time, the energy transfer under the non-conservative forces poses a potentially very powerful failure mechanism for nanoscale conductors.

The interaction of the atomic motion with the electronic subsystem can lead further to velocity-dependent forces on nuclei. One of them, sometimes termed electronic friction, is an effective damping force, resulting from the loss of energy from the atomic motion due to the excitation of electrons. (The converse effect - spontaneous phonon emission by the current-carrying electrons - is at the root of Joule heating and is one of the most difficult effects to capture theoretically.) Another velocity-dependent force, proposed by our collaborators in Denmark, originates strictly from the current. The dynamics of the atoms under current is the result of the interplay between all these effects. Understanding them in turn is essential in gauging the stability, functionality and applicability of these systems as nanoscale devices, against effects such as local heating, electromigration, or the enormous energy transfer from current to the atomic dynamics that can take place under the recently proposed non-conservative current-induced forces above.

A considerable part of these questions can be understood by treating the atomic motion classically. In collaboration with colleagues from Denmark and China, however, we have been able to arrive at an effective driven quantum Liouville equation for the atomic motion under current, that subsumes all of the aforementioned effects.

The aim of this project is to study the properties of this equation and bring out the physics it describes. To this end, we will begin with the more familiar classical description of the nuclei, and gain further experience with the effects that current-induced forces can have on atomic wires. We will then move on to the quantum Liouville equation and solve it numerically for simple model systems, together with a pen-and-paper analysis of the effects that it generates.

Strategically, the project has aspects from Condensed Matter Physics and the electronic properties of low-dimensional systems, and Quantum Devices, Components and Systems and the understanding of novel energy conversion mechanisms in quantum conductors.

This work is envisaged as a collaboration with our colleagues at the Niels Bohr Institute and the Technical University of Denmark in Copenhagen. We will benefit further from our long-standing links with leading experimentalists in atomic-scale conductors at the University of Leiden.