Carbon nanotubes and graphene allow fabricating outstanding nanomechanical resonators. They hold promise for various scientific and technological applications, including sensing of mass, force, and charge, as well as the study of quantum phenomena at
the mesoscopic scale. Here, we have discovered that the dynamics of nanotube and graphene resonators is in fact highly exotic. We propose an unprecedented scenario where mechanical dissipation is entirely determined by nonlinear damping. As a striking consequence, the quality factor Q strongly depends on the amplitude of the motion. This scenario is radically different from that of other resonators, whose dissipation is dominated by a linear damping term. We believe that the difference stems from the reduced dimensionality of carbon nanotubes and graphene. Besides, we exploit the nonlinear nature of the damping to improve the figure of merit of nanotube/graphene resonators.
We have investigated electron dynamics in top gated graphene by measuring the gate admittance of a diffusive graphene capacitor in a broad frequency range as a function of carrier density. The density of states, conductivity and diffusion constant ar
e deduced from the low frequency gate capacitance, its charging time and their ratio. The admittance evolves from an RC-like to a skin-effect response at GHz frequency with a crossover given by the Thouless energy. The scattering time is found to be independent of energy in the 0 - 200 meV investigated range at room temperature. This is consistent with a random mass model for Dirac Fermions.
The high-frequency transconductance and current noise of top-gated single carbon nanotube transistors have been measured and used to investigate hot electron effects in one-dimensional transistors. Results are in good agreement with a theory of 1-dim
ensional nano-transistor. In particular the prediction of a large transconductance correction to the Johnson-Nyquist thermal noise formula is confirmed experimentally. Experiment shows that nanotube transistors can be used as fast charge detectors for quantum coherent electronics with a resolution of $13mathrm{mu e/sqrt{Hz}}$ in the 0.2-$0.8 mathrm{GHz}$ band.
