Charge-memory polaron effect in molecular junctions

The charge-memory effect, bistability, and switching between charged and neutral states of a molecular junction, as observed in recent scanning-tunneling microscope (STM) experiments, is considered within a minimal polaron model. We show that in the case of strong electron-vibron interaction, the rate of spontaneous quantum switching between charged and neutral states is exponentially suppressed at zero bias voltage but can be tuned through a wide range of finite switching time scales upon changing the bias. We further find that, while junctions with symmetric voltage drop give rise to random switching at finite bias, asymmetric junctions exhibit hysteretic behavior, enabling controlled switching. Lifetimes and charge-voltage curves are calculated by the master-equation method for weak coupling to the leads and at stronger coupling by the equation-of-motion method for nonequilibrium Green’s functions.

Figure 1

(Color online) (a) The energy diagram of the single-level electron-vibron model, coupled to the left and right leads (or tip and substrate in the case of STM). (b) Franck-Condon matrix elements $M_{0m}$ for weak ($g=0.1$, squares), intermediate ($g=1$, triangles), and strong ($g=10$, circles) interactions.

Figure 2

Inverse lifetime ${\left(\tau \Gamma \right)}^{-1}$ of the neutral state (thin solid line) and the charged state (thick gray solid line) as a function of $\lambda /{\omega }_0$ at ${ϵ}_0={\lambda }^2/2{\omega }_0$ and the same at ${ϵ}_0=0.9{\lambda }^2/{\omega }_0$ (dashed lines); $kT=0.1{\omega }_0$.

Figure 3

Inverse lifetime ${\left(\tau \Gamma \right)}^{-1}$ as a function of normalized voltage $eV/{\omega }_0$ for the asymmetric junction $\left(\eta =0\right)$ at $\lambda /{\omega }_0=5$ and ${ϵ}_0={\lambda }^2/2{\omega }_0$ for the neutral state (thin solid line) and the charged state (thick gray solid line) and the same for the symmetric junction ($\eta =0.5$, dashed lines). Inset: random switching between bistable states (dashed line) and single switching into the stable state (full line) after a sudden change in the voltage.

Figure 4

Population of the neutral state as a function of normalized voltage $eV/{\omega }_0$ in the asymmetrical junction $\left(\eta =0\right)$ at $\lambda /{\omega }_0=5$ and ${ϵ}_0={\lambda }^2/2{\omega }_0$ for fast voltage sweep (thin solid line), for slower sweep (thick gray solid line), and in the adiabatic limit (dashed line). Inset: sketch of voltage time dependence.

Figure 5

Average number of electrons at ${\Gamma }_L={\Gamma }_R=5{\omega }_0$ as a function of normalized voltage $eV/{\omega }_0$ for the asymmetric junction, $\eta =0$ (thin solid line), and for the symmetric junction, $\eta =0.5$ (dashed line), for $\lambda /{\omega }_0=5$ and ${ϵ}_0={\lambda }^2/{\omega }_0$.