Vibrationally mediated control of single-electron transmission in weakly coupled molecule-metal junctions

We propose a mechanism which allows one to control the transmission of single electrons through a molecular junction. The principle utilizes the emergence of transmission sidebands when molecular vibrational modes are coupled to the electronic state mediating the transmission. We will show that if a molecule-metal junction is biased just below a molecular resonance, one may induce the transmission of a single electron by externally exciting a vibrational mode of the molecule. The analysis is quite general but requires that the molecular orbital does not hybridize strongly with the metallic states. As an example we perform a density-functional theory analysis of a benzene molecule between two Au(111) contacts and show that exciting a particular vibrational mode can give rise to transmission of a single electron.

Figure 1

(Color online) A molecule between two metal contacts is represented by a resonant state (for example, the lowest unoccupied molecular orbital) and a vibrational potential. If the molecule is initially vibrationally excited, an electron below the resonance may tunnel through the molecule by absorbing a quantum of vibration. When the molecule is initially in its vibrational ground state, transmission is not possible.

Figure 2

(Color online) Transmission probabilities calculated from Eq. (1) as a function of incoming electron energy with ${\Gamma }_L={\Gamma }_R=0.04\hslash \omega$ and $\lambda =0.4\hslash \omega$. Below the resonance energy ${\epsilon }_0$, the ground-state transmission functions $T_{00}\left({\epsilon }_i\right)$ and $T_{01}\left({\epsilon }_i\right)$ essentially vanish. The inset shows the lower sideband, where stimulated emission of a vibrational quantum $T_{10}\left({\epsilon }_i\right)$ is the dominating transmission channel.

Figure 3

(Color online) Ratio of elastic and inelastic transmission probabilities in the first vibrationally excited state. At weak coupling, the elastic transmission $T_{11}$ goes to zero indicating that a vibrational excitation results in only a single electron being transmitted.

Figure 4

(Color online) The principle of single-electron transmission. A small bias is applied such that the bias window just covers the resonance: $e{V}_B\sim \Gamma$ and a gate voltage is tuned such that the resonance is located at ${\epsilon }_0\sim {\mu }_L-e{V}_B/2+\hslash \omega$. In the vibrational ground state, the transmission function $T_{00}$ (solid line) is zero in the bias window. Exciting the first vibrational state changes the transmission function which is dominated by the inelastic part $T_{10}$ (dashed line) in the bias window. A vibrational excitation of the molecule will thus result in a single electron being transmitted.

Figure 5

(Color online) Adsorption energy of benzene on Au(111) as a function of distance to the surface, calculated with three different functionals. The molecular states are weakly hybridized with the metallic states and only the functional including the van der Waals interaction gives the correct adsorption well.

Figure 6

(Color online) Left: the LUMO of benzene. Right: the vibrational mode of highest energy which can be excited by a transient occupation of the LUMO.