  We report on a simple method to fabricate high-frequency nanotube mechanical
resonators reproducibly. We measure resonance frequencies as high as 4.2 GHz
for the fundamental eigenmode and 11 GHz for higher order eigenmodes. The
high-frequency resonances are achieved using short suspended nanotubes and by
introducing tensile stress in the nanotube. These devices allow us to determine
the coefficient of the thermal expansion of an individual nanotube, which is
negative and is about -0.7E-5 1/K at room temperature. High-frequency
resonators made of nanotubes hold promise for mass sensing and experiments in
the quantum limit.
