Vibrationally dependent electron-electron interactions in resonant electron transport through single-molecule junctions

We investigate the role of electronic-vibrational coupling in resonant electron transport through single-molecule junctions, taking into account that the corresponding coupling strengths may depend on the charge and excitation state of the molecular bridge. Within an effective-model Hamiltonian approach for a molecule with multiple electronic states, this requires to extend the commonly used model and include vibrationally dependent electron-electron interaction. We use Born-Markov master equation methods and consider selected models to exemplify the effect of the additional interaction on the transport characteristics of a single-molecule junction. In particular, we show that it has a significant influence on local cooling and heating mechanisms, it may result in negative differential resistance, and it may cause pronounced asymmetries in the conductance map of a single-molecule junction.

Figure 1

Scheme of potential energy surfaces of the molecular bridge corresponding to the ground state (GS) and first excited state (ES) of the neutral molecule, its anion, and the dianion. The equilibrium geometry of the respective molecular states is marked by dashed vertical lines of the same color, and the displacement of the equilibrium geometry with respect to the ground state of the neutral molecule is shown by black arrows.

Figure 2

Conductance of model system ${\mathrm{EFF}}^{*}$ as a function of bias voltage and vibrationally coupled electron-electron coupling strength $W$.

Figure 3

(a) Current-voltage characteristics for the model system EFF. (b) Vibrational excitation as a function of bias voltage for the system EFF. The vertical dashed lines in both plots mark the onset of resonant transport through the corresponding molecular electronic states.

Figure 4

(a) Current-voltage characteristics for the model system STMSETUP. (b) Vibrational excitation as a function of bias voltage for the system STMSETUP. The vertical dashed lines in both plots mark the onset of resonant transport through the corresponding molecular electronic states. The inset in panel (b) shows an enlargement of the region $\mathrm{\Phi }\approx 2({\overline{\epsilon }}_{1/2}+\overline{U})$.

Figure 5

Current-voltage characteristics of model system DARKST. The vertical dashed lines mark the onset of resonant transport through molecular electronic states.

Figure 6

Conductance as a function of bias and gate voltage for the system EFF for $W=0,\pm 0.05$ eV. Notice the different scale used for negative conductances.

Figure 7

Conductance as a function of bias and gate voltage for the system ASYMM for $W=0,\pm 0.05$ eV. Notice the different scaling for negative conductances.