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A hallmark of mechanical resonators made from a single nanotube is that the resonance frequency can be widely tuned. Here, we take advantage of this property to realize parametric amplification and self-oscillation. The gain of the parametric amplification can be as high as 18.2 dB and tends to saturate at high parametric pumping due to nonlinear damping. These measurements allow us to determine the coefficient of the linear damping force. The corresponding damping rate is lower than the one obtained from the line shape of the resonance (without pumping), supporting the recently reported scenario that describes damping in nanotube resonators by a nonlinear force. The possibility to combine nanotube resonant mechanics and parametric amplification holds promise for future ultralow force sensing experiments.

We report on microwave operation of top-gated single carbon nanotube transistors. From transmission measurements in the 0.1-1.6 GHz range, we deduce device transconductance gm and gate-nanotube capacitance Cg of micro- and nanometric devices. A large and frequency-independent gm approximately 20 microS is observed on short devices, which meets the best dc results. The capacitance per unit gate length of 60 aF/microm is typical of top gates on a conventional oxide with epsilon approximately 10. This value is a factor of 3-5 below the nanotube quantum capacitance which, according to recent simulations, favors high transit frequencies fT=gm/2piCg. For our smallest devices, we find a large fT approximately 50 GHz with no evidence of saturation in length dependence.