Current-induced nonequilibrium vibrations in single-molecule devices

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 $\ensuremath{\lambda}$ within a minimal model. Remarkably, the width of the phonon distribution diverges as $\ensuremath{\sim}{\ensuremath{\lambda}}^{\ensuremath{-}\ensuremath{\alpha}}$ when the coupling decreases, with voltage-dependent, noninteger exponents $\ensuremath{\alpha}$. 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.