Electronic Transport in Fullerene ${\mathrm{C}}_{20}$ Bridge Assisted by Molecular Vibrations

The effect of molecular vibrations on electronic transport is investigated with the smallest fullerene ${\mathrm{C}}_{20}$ bridge, utilizing the Keldysh nonequilibrium Green’s function techniques combined with the tight-binding molecular-dynamics method. Large discontinuous steps appear in the differential conductance when the applied bias voltage matches particular vibrational energies. The magnitude of the step is found to vary considerably with the vibrational mode and to depend on the local electronic states besides the strength of electron-vibration coupling. On the basis of this finding, a novel way to control the molecular motion by adjusting the gate voltage is proposed.

Figure 1

Schematic diagram of the ${\mathrm{C}}_{20}$ fullerene connected to Au electrodes by two springs. The ${\mathrm{C}}_{20}$ with $D_{3d}$ point-group symmetry contains four distinct bond lengths among nonequivalent carbon atoms labeled $a$, $b$, and $c$ (or $c^{\prime }$, $c^{\prime \prime }$).

Figure 2

The differential conductance in the unit of $2e^2/h$. Solid and dashed curves represent the total differential conductance and its elastic component, respectively. The arrows indicate particular discontinuous steps. The inset represents the total and elastic electronic current through the ${\mathrm{C}}_{20}$ bridge.

Figure 3

The scattering intensity of electrons due to molecular vibrations of the ${\mathrm{C}}_{20}$ bridge. The arrows indicate the particular peaks that coincide with the discontinuous steps in Fig. 2.

Figure 4

The electron density of $\mathrm{Au}\mathrm{\text{−}}{\mathrm{C}}_{20}\mathrm{\text{−}}\mathrm{Au}$ at (a) $-1.5\mathrm{eV}$ and (b) 0 eV (the Fermi level), and (c) the scattering intensity for the shuttle motion of ${\mathrm{C}}_{20}$. The electron density is indicated by the red shading on the atom spheres.