We study the quantum dynamics of a symmetric nanomechanical graphene resonator with degenerate flexural modes. Applying voltage pulses to two back gates, flexural vibrations of the membrane can be selectively actuated and manipulated. For graphene, n
onlinear response becomes important already for amplitudes comparable to the magnitude of zero point fluctuations. We show, using analytical and numerical methods, that this allows for creation of cat-like superpositions of coherent states as well as superpositions of coherent cat-like non-product states.
We propose a scheme to measure the mass of a single particle using the nonlinear response of a 2D nanoresonator with degenerate eigenmodes. Using numerical and analytical calculations, we show that by driving a square graphene nanoresonator into the
nonlinear regime, simultaneous determination of the mass and position of an added particle is possible. Moreover, this scheme only requires measurements in a narrow frequency band near the fundamental resonance.
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.
