Dr. Aniruddha Chakraborty

In an interesting experiment, Park et al. [1] reported a three-electrode transistor made using a single C60 molecule. Experiment shows that the nanomechanical oscillations of C60 trapped between the two electrodes can be excited by the passage of current through the system. There have been attempts to model the process [2-4].
The experimental and theoretical work lead to the conclusion that the formation of C60- results in a shift of the equilibrium position by about 3-4 pm [1,3]. It was suggested that this shift arise due to the image interaction, though the details of the geometry that would lead to such a shift is never discussed [1,3]. Unfortunately, there is no information available on the way the C60 is trapped between the two electrodes. If the two electrodes are planar, and if the C60 is sitting symmetrically between the two, then the formation of C60- cannot lead to a shift in the equilibrium position.
On the other hand, if it is not sitting symmetrically, then its distance from the other electrode would be large and this would lead to only very small currents, thus ruling out this possibility. We point out that even in the symmetric situation, the distance dependence of the electron hopping matrix element can lead to the excitation of center of mass oscillation, a mechanism that has never been considered earlier [1-4]. Using the decay of the wave function at the Fermi level to model the decay of the matrix element, we find that this effect is roughly equivalent to displacing the equilibrium position by 0.165 pm, and this alone is not able to explain the experimental observations. Therefore, we consider a situation where one of the electrodes has a hemispherical protrusion as a model for non-planar electrodes. We find that if C60 is trapped between a hemispherical protrusion of radius 3.5 Å and a planar surface, then the shift in equilibrium position on forming C60- is about 1.7 pm and this alone, would not again account for the experimental observations. However, this combined with the position dependence hopping matrix element seems to explain the experimental data qualitatively [5]. For quantitative agreemen with experiments, it seems necessary to consider perhaps the non-uniformity of the charge distribution in C60- caused by the image interaction or more complex electrode geometries.

  C60 - Single Molecule Transistor

References

1. H. Park, J. Park, A. K. L. Lim, E. H. Anderson, A. P. Alivisatos and P. L. McEuen, Nature, 407, 57 (2000).
2. D. M. Ventra, S. T. Pantelides and N. D. Lang, Phys. Rev. Lett. 84, 979 (2000).
3. D. Boese and H. Schoeller, Europhy. Lett. 54, 668 (2001).
4. L. Y. Gorelik, A. Isacsson, M. V. Voinova, B. Kasemo, R. I. Shekhter and M, Phys. Rev. Lett. 80, 4526 (1998).
5. Aniruddha Chakraborty, Keshav Kumar, and K. L. Sebastian, Phys. Rev. B 68, 085411 (2003).