Vibration-mediated correlation effects in the transport properties of a benzene molecule

We theoretically analyze correlation effects on the transport properties of a benzene molecule that are mediated by interactions between the motion of the nuclei and the transmitted charge. We focus on the lowest-lying molecular vibrational mode which allows us to derive an analytic expression for the current. The results provide transparent interpretations of various features of the highly nonlinear current-voltage characteristics, which is experimentally accessible through resonant inelastic electron-tunneling spectroscopy.

Figure 1

(a) Illustration of the phonon breathing mode in a benzene molecule (red spheres), which is coupled to metallic leads (blue spheres). (b) The bias voltage $V_b$ induces a current $j$ that is significantly modified by the interaction between the nuclear motion and the charge. At low $V_b$ the current is suppressed,[6] see the inset, whereas, at large $V_b$ strong nonlinear behavior leads to a stepwise increase in the current, also manifesting in (c) the conductance and (d) the differential shot noise through multiple equally spaced peaks. The data are evaluated at $T=10\mathrm{K}$.

Figure 2

Temperature dependence of (a) the current, (b) the conductance, and (c) the differential shot noise versus bias voltage $V_b$ curves. At temperatures $T$ much lower than the phonon energy ${\omega }_{\mu }=0.086\mathrm{eV}$, which is the smallest energy scale in Eq. (1), the phonon-mediated steps and peaks, respectively, are pronounced and clearly visible. For increasing temperature these features are washed out, and at room temperature $T=300\mathrm{K}$, hardly any remain.

Figure 3

(a) Current as a function of the bias voltage $V_b$ and the gate voltage $V_g$ and (b) corresponding stability diagram (i.e., differential conductance). The electron-phonon interaction increases the area of the central diamond and induces a splitting of the lines in the stability diagram. (c) Fowler-Nordheim plots for a few selected values of the gate voltage $V_g$ specified in the legend. Data evaluated for $T=10\mathrm{K}$.