Current-induced nonequilibrium vibrations in single-molecule devices

TL;DR

This paper analytically studies how finite-bias electron transport causes nonequilibrium vibrations in single molecules, revealing divergence in phonon distribution width at weak coupling and implications for molecular stability.

Contribution

It introduces a Fokker-Planck approach to derive scaling forms for nonequilibrium phonon distributions in molecular devices with weak electron-phonon coupling.

Findings

Phonon distribution width diverges as coupling decreases.

Non-integer voltage-dependent exponents characterize the divergence.

Perturbation theory breaks down for strong nonequilibrium phonon states.

Abstract

Finite-bias electron transport through single molecules generally induces nonequilibrium molecular vibrations (phonons). By a mapping to a Fokker-Planck equation, we obtain analytical scaling forms for the nonequilibrium phonon distribution in the limit of weak electron-phonon coupling $\lambda$ within a minimal model. Remarkably, the width of the phonon distribution diverges as $\sim\lambda^{-\alpha}$ when the coupling decreases, with voltage-dependent, non-integer exponents $\alpha$. This implies a breakdown of perturbation theory in the electron-phonon coupling for fully developed nonequilibrium. We also discuss possible experimental implications of this result such as current-induced dissociation of molecules.