Bistability signatures in nonequilibrium charge transport through molecular quantum dots

We investigate the transient nonequilibrium dynamics of a molecular junction biased by a finite voltage and strongly coupled to internal vibrational degrees of freedom. Using two different, numerically exact techniques, diagrammatic Monte Carlo and the multilayer multiconfiguration time-dependent Hartree method, we show that the steady-state current through the junction may depend sensitively on the initial preparation of the system, thus revealing signatures of bistability. The influence of the bias voltage and the transient dynamics on the phenomenon of bistability is analyzed. Furthermore, a possible relation to the phenomenon of stochastic switching in nanoelectromecanical devices is discussed.

Figure 1

Comparison of ML-MCTDH-SQR (lines) and diagMC data (symbols) for an initially empty (black) and occupied (red [gray]) dot for $I\left(t\right)$ (circles and solid lines), $I_L\left(t\right)$ (squares and dashed lines), and $-I_R\left(t\right)$ (diamonds and dotted lines). The main graph shows the average current for ${\epsilon }_D=4.7\Gamma$, $V=1.25\Gamma$, ${\Gamma }_{\alpha }\left(\epsilon \right)=\Gamma \sqrt{1-{(\epsilon /{\epsilon }_c)}^2}$ for $\left|\epsilon \right|⩽{\epsilon }_c$ with bandwidth $2{\epsilon }_c=50\Gamma$ (semielliptic band) and an Ohmic spectral density $J\left(\omega \right)=2\pi \omega \exp (-\omega /{\omega }_c)$ with ${\omega }_c=0.775\Gamma$ at zero temperature; filled and open symbols refer to $I\left(t\right)$ and $[I_L\left(t\right)-I_R\left(t\right)]/2$, respectively. The inset displays the different time scales on which $I\left(t\right)$, $I_L\left(t\right)$, and $I_R\left(t\right)$ reach the stationary regime, while the upper panel demonstrates that all currents converge to the same stationary value.

Figure 2

Current $I\left(t\right)$ for ${\epsilon }_D=-5\Gamma$, ${\Gamma }_{\alpha }\left(\epsilon \right)=\Gamma /2$ for $\left|\epsilon \right|⩽{\epsilon }_c$ (flat band), and a single phonon mode with ${\lambda }_0=8\Gamma$ and ${\omega }_0=4\Gamma$, for an initially empty (black) and occupied (red [gray]) dot at zero temperature. Open symbols refer to diagMC data for a smooth switch on of the tunneling coupling, $\Gamma (\epsilon ,t)={\sin }^2[\pi t/\left(2{\tau }_{\text{s}w}\right)]\Gamma \left(\epsilon \right)$ for $t⩽{\tau }_{\text{s}w}$ ($=8{\Gamma }^{-1}$ for $V=5\Gamma$ and $35\Gamma$, else $6{\Gamma }^{-1}$), while filled symbols refer to an instantaneous switch on. The bandwidth is $2{\epsilon }_c=41\Gamma$ for $V=35\Gamma$, else $26\Gamma$.

Figure 3

Similar to Fig. 2 but with the ML-MCTDH-SQR result for the parameters: ${\epsilon }_D=-2.5\Gamma$, ${\omega }_0=\Gamma /8$, ${\lambda }_0=\Gamma$, and a bandwidth $2{\epsilon }_c=20\Gamma$. Insets show magnified versions of the same plots in the stationary regime.