Origins of asymmetric charge transport properties of weakly coupled molecular junctions

Understanding charge transport properties of a molecular junction plays a crucial role in the possible application of such devices. In this work we present a theoretical study on the transport properties of molecular transistors in the sequential tunneling regime. Special attention is paid to the origins of the asymmetries in the charge transport properties as presented by the commonly measured conductance stability diagrams (two-dimensional plots of the differential conductance against gate and bias voltages). It is found that both the external factors, including the bias coupling constant and the coupling strength between the molecule and the electrodes, and the intrinsic molecular properties such as the frequency differences between different charging states, the anharmonicity of the potential energy surface, and the mode-mixing effect can lead to asymmetric conductance stability diagrams. Especially, we show that the uneven bias coupling between the molecule and the two electrodes can result in strong current rectifications. These results successfully reproduce the change in rectification directions of molecular diodes as observed in a recent experiment [L. Yuan et al., Nat. Commun. 6, 6324 (2015)]. The differences in the asymmetric stability diagram caused by the studied factors are also discussed, which helps us to correctly interpret the experimental results.

Figure 1

(a) Schematic drawing of the single-molecule transistor studied in the present work. The molecule ($M$) was capacitively coupled to the left ($L$), right ($R$), and gate electrodes with the corresponding electrode capacitances $C_L$, $C_R$, and $C_G$ [14]. (b) The corresponding energetic diagrams of the transistor. The molecule is represented by two charging states ($|0\rangle$ and $|1\rangle$), each with a number of vibrational levels. (c) A typical symmetric conductance stability diagram computed for harmonic potentials with $\alpha =\beta =0.5$, ${\omega }_1={\omega }_2=1000{\text{cm}}^2$, ${\gamma }^L={\gamma }^R=1.0\mu \mathrm{eV}$, $\mathrm{\Delta }Q=41.90\text{a.u.}$

Figure 2

Conductance stability diagrams simulated with different values of the bias coupling constant $\alpha$. All of the other parameters are the same as in Fig. 1.

Figure 3

$I\text{−}{V}_b$ curves calculated at three different bias coupling constants under $V_g=-9\hslash \omega /e$: (a) $\alpha =0.2$, (b) $\alpha =0.5$, and (c) $\alpha =0.8$. The changes in the conductance in (a) and (c) are indicated by the vertical dashed lines in Figs. 2 and 2(g), respectively. (d)–(f) The experimental results from Ref. [19]. The experimental results were obtained by tuning the length of the linker groups (alkyl chains) between the conducting unit of the molecule and the electrodes.

Figure 4

(a)–(d) Conductance stability diagrams calculated with different values of ${\gamma }^L$. (e)–(h) $I\text{−}{V}_b$ curves with $V_g=-5\hslash \omega /e$. (i)–(l) Steady-state population of the ground vibrational energy level in the two electronic states at $V_g=-5\hslash \omega /e$ as a function of the bias voltage. All of the other parameters are the same as in Fig. 1.

Figure 5

Effect of frequency changes on the conductance stability diagrams: (a) ${\omega }_2={\omega }_1$ and (b) ${\omega }_2=1.2{\omega }_1$. (c) The $G\text{−}{V}_b$ curves obtained with $V_g=-3\hslash \omega /e$. In the simulations $\alpha$ has been set to 0.5. The molecule-electrode coupling has also been set to be symmetric with ${\gamma }^L={\gamma }^R$.

Figure 6

(a) Conductance stability diagram computed for the model transistor with the Morse potential. (b) $G\text{−}{V}_b$ curve obtained with $V_g=3\hslash \omega /e$. All of the other parameters are the same as in Fig. 1.

Figure 7

Conductance stability diagrams simulated with different rotation angles: (a) $\theta =0$ and (b) $\theta =\pi /4$. (c) The $G\text{−}{V}_b$ curves obtained at $V_g=-3\hslash \omega /e$. The detailed transition assignments are marked beside the peak position. Two vibrational modes with frequencies of 1000 and 1200 ${\mathrm{cm}}^{-1}$ are included in each of the two electronic states. $\mathrm{\Delta }{Q}_1=41.90$ a.u., $\mathrm{\Delta }{Q}_2=0$. All other parameters are the same as in Fig. 1.