Phonon Driven Nonlinear Electrical Behavior in Molecular Devices

Electronic transport in a model molecular device coupled to local phonon modes is theoretically analyzed. The method allows for obtaining an accurate approximation of the system’s quantum state irrespective of the electron and phonon energy scales. Nonlinear electrical features emerge from the calculated current-voltage characteristics. The quantum corrections with respect to the adiabatic limit characterize the transport scenario, and the polaronic reduction of the effective device-lead coupling plays a fundamental role in the unusual electrical features.

Figure 1

GS energy estimate as a function of the parameters $n,\theta$ (upper panel) for a fixed value of ${\tau }^2=0.6933$. The model parameters are $W=12$, $\Delta =1$, $\lambda =3$, ${\epsilon }_0=3$. GS energy estimate in the BO limit as a function of $n$ (lower panel) for the same set of model parameters.

Figure 2

Optimal variational parameter estimates as functions of the unperturbated ${\epsilon }_0$ molecular energy level for different sets of $W$, $\Delta$, $\lambda$. Black lines indicate $n$, blue lines $\vartheta$, and red lines ${\tau }^2$. The estimate of the level filling $n$ in the adiabatic limit is also shown as a dashed black line.

Figure 3

Level filling for the different stable solutions as a function of the applied bias $V_{\mathrm{bias}}$ estimated by means of our method (solid line) and using the adiabatic approximation (dashed lines). The parameter sets are $W=20$, ${\Delta }_L={\Delta }_R=1$, $\lambda =6.5$, ${\epsilon }_0=6.4$. Outer roots are plotted in black and blue, inner roots in red.

Figure 4

Current-voltage characteristics of the different stable solutions estimated by means of our method (solid line) and using the adiabatic approximation (dashed lines). The parameters are $W=20$, ${\Delta }_L={\Delta }_R=1$, $\lambda =6.5$, ${\epsilon }_0=6.4$. Outer roots are plotted in black and blue, inner roots in red. Outer root for $V>0$ obtained for the same set of parameters but avoiding the wideband limit and including electron correlation ($U=7$) are shown as magenta and green solid lines, respectively. In the inset we show the coupling constant reduction ${\tilde{\Delta }}_L/{\Delta }_L={\tilde{\Delta }}_R/{\Delta }_R$ (solid line) and the shifted energy level ${\tilde{\epsilon }}_0$ (dashed line) as a function of the applied bias $V_{\mathrm{bias}}>0$ for the inner optimal stable solution.