We study nanomechanical resonators with frequency fluctuations due to diffusion of absorbed particles. The diffusion depends on the vibration amplitude through inertial effect. We find that, if the diffusion coefficient is sufficiently large, the res
onator response to periodic driving displays bistability. The lifetime of the coexisting vibrational states scales exponentially with the diffusion coefficient. It also displays a characteristic scaling dependence on the distance to bifurcation points.
We study resonant response of an underdamped nanomechanical resonator with fluctuating frequency. The fluctuations are due to diffusion of molecules or microparticles along the resonator. They lead to broadening and change of shape of the oscillator
spectrum. The spectrum is found for the diffusion confined to a small part of the resonator and where it occurs along the whole nanobeam. The analysis is based on extending to the continuous limit, and appropriately modifying, the method of interfering partial spectra. We establish the conditions of applicability of the fluctuation-dissipation relations between the susceptibility and the power spectrum. We also find where the effect of frequency fluctuations can be described by a convolution of the spectra without these fluctuations and with them as the only source of the spectral broadening.
Graphene nanoribbons provide an opportunity to integrate phase-coherent transport phenomena with nanoelectromechanical systems (NEMS). Due to the strain induced by a deflection in a graphene nanoribbon resonator, coherent electron transport and mecha
nical deformations couple. As the electrons in graphene have a Fermi wavelength lambda ~ a_0 = 1.4 {AA}, this coupling can be used for sensitive displacement detection in both armchair and zigzag graphene nanoribbon NEMS. Here it is shown that for ordered as well as disordered ribbon systems of length L, a strain epsilon ~ (w/L)^2 due to a deflection w leads to a relative change in conductance delta G/G ~ (w^2/a_0L).
We study, numerically and analytically, a model of a one-dimensional array of carbon nanotube resonators in a two-terminal configuration. The system is brought into resonance upon application of an AC-signal superimposed on a DC-bias voltage. When th
e tubes in the array are close to each other, electrostatic interactions between tubes become important for the array dynamics. We show that both transverse and longitudinal parametric resonances can be excited in addition to primary resonances. The intertube electrostatic interactions couple modes in orthogonal directions and affect the mode stability.
We theoretically investigate electron transport through corrugated graphene ribbons and show how the ribbon curvature leads to an electronic superlattice with a period set by the corrugation wave length. Transport through the ribbon depends sensitive
ly on the superlattice band structure which, in turn, strongly depends on the geometry of the deformed sheet. In particular, we find that for ribbon widths where the transverse level separation is comparable to the the band edge energy, a strong current switching occurs as function of an applied backgate voltage. Thus, artificially corrugated graphene sheets or ribbons can be used for the study of Dirac fermions in periodic potentials. Furthermore, this provides an additional design paradigm for graphene-based electronics.
