pss(b) accepted: Negative frequency tuning of a carbon nanotube nano-electromechanical resonator under tension

One of the measurements in the MSc project of Sabine Kugler revealed a very particular carbon nanotube nano-electromechanical resonator. Usually the mechanical resonance frequency is tuned up to higher values by applying a gate voltage to the back gate: the larger charge on the nanotube and the larger forces between gate and nanotube cause mechanical tension within the nanotube, and exactly the same way as when tuning a guitar or piano string this translates to a higher resonance frequency. Curiously, here a very strong effect to the opposite can be observed; we can tune the resonance frequency to 75% of its zero-gate voltage value by applying a gate voltage! This is even more astonishing since we can conclude from the higher harmonics of our vibration mode that the nanotube is under tension.
The observed effect can be explained via so-called electrostatic softening of the vibration mode. Let us assume that the carbon nanotube is very close to the gate and vibrates towards and away from it. The capacitance between gate and nanotube varies within one oscillation cycle, and thereby the electrostatic force between these two obtains an additional position-dependent component. This can be seen as an electrodynamic contribution to the spring constant of the resonator; it is negative and thereby decreases the resonance frequency. We can estimate the size of this effect and obtain indeed consistent values for our sample geometry.

"Negative frequency tuning of a carbon nanotube nano-electromechanical resonator under tension"
P. L. Stiller, S. Kugler, D. R. Schmid, C. Strunk, and A. K. Hüttel
accepted for publication by physica status solidi (b), arXiv:1304.5092 (PDF)