Carbon nanotubes: Nonlinear high-Q resonators with strong coupling to single-electron tunneling

Carbon nanotubes (CNTs) are nonlinear high-Q resonators with strong coupling to single-electron tunneling. We begin by describing several methods to detect the flexural motion of a CNT resonator. Next, we illustrate how single-electron tunneling in quantum dot CNT resonators leads to sharp dips in the mechanical resonance frequency and significant damping. We discuss four different contributions to the nonlinear oscillation of a CNT resonator: beam-like mechanical nonlinearity, nonlinearity due to gate-induced mechanical tension, electrostatic nonlinearity, and nonlinearity due to single-electron tunneling, and provide quantitative estimates of their strengths. Finally, we show how the large response of the resonance frequency of a CNT resonator to a change in gate voltage or tension makes CNT resonators ideally suited for parametric excitation and for studying the coupling between different mechanical modes.