Intermittent polaron dynamics: Born-Oppenheimer approximation out of equilibrium

We consider a model of a molecular switch that consists of an electronic orbital strongly interacting with a local vibrational mode. The strong polaronic interaction prevents perturbative treatment of the problem. Instead, we find that in an adiabatic regime when the electronic dynamics is faster than the vibrational frequency, it is possible to provide a fully nonperturbative treatment of the nonequilibrium properties of the system. The results shows intermittent switching between bistable states of the oscillator with an effective random telegraph noise.

Figure 1

Symbolic representation of system’s energetics: The potential curve of the mechanical degree of freedom versus the electronic energy levels.

Figure 2

(a) Diagrammatic resummation of the effective action of the oscillator; the dressed bubbles represent contributions to the effective potential of the oscillator, dissipation, and noise caused by the electrons. (b) Renormalization of the electronic Green’s function by the adiabatic oscillator; here vertex $x_c$ is effectively time independent.

Figure 3

Typical $I$-$V$ curve of the molecular junction in the polaronic regime (solid line); the dashed lines correspond to currents, when the “oscillator” occupies different wells. Inset (a): Schematic representation of the temporal dynamics of the current; for sufficiently small voltages the “oscillator” spends most of the time in a deeper well and occasionally jumps to a shallower well; the mean time-scales ${\tau }_{1,2}$ are given by Eq. (15). Inset (b): same as inset (a), but at higher voltages. Now the probability to occupy the shallower well, and the switching rate increase due to higher effective temperature, e.g., Eq. (15).