Scattering theory of current-induced forces in mesoscopic systems

TL;DR

This paper presents a scattering theory for current-induced forces in mesoscopic conductors, capturing both equilibrium and nonequilibrium effects, including non-conservative and velocity-dependent forces, with applications to molecular junctions.

Contribution

It introduces a comprehensive scattering framework to analyze current-induced forces on mechanical degrees of freedom in mesoscopic systems, including nonequilibrium effects and Langevin dynamics.

Findings

Mechanical forces include non-conservative and Lorentz-like components.

The theory predicts limit-cycle dynamics in a molecular junction model.

Current-induced forces can be negative, affecting stability.

Abstract

We develop a scattering theory of current-induced forces exerted by the conduction electrons of a general mesoscopic conductor on slow "mechanical" degrees of freedom. Our theory describes the current-induced forces both in and out of equilibrium in terms of the scattering matrix of the phase-coherent conductor. Under general nonequilibrium conditions, the resulting mechanical Langevin dynamics is subject to both non-conservative and velocity-dependent Lorentz-like forces, in addition to (possibly negative) friction. We illustrate our results with a two-mode model inspired by hydrogen molecules in a break junction which exhibits limit-cycle dynamics of the mechanical modes.