Andreas Isacsson

Continuum elastic modeling of graphene resonators

Starting from an atomistic approach, we have derived a hierarchy of successively more simplified continuum elasticity descriptions for modeling the mechanical properties of suspended graphene sheets. We find that already for deflections of the order of 0.5 A a theory that correctly accounts for nonlinearities is necessary and that for many purposes a set of coupled Duffing-type equations may be used to accurately describe the dynamics of graphene membranes. The descriptions are validated by applying them to square graphene-based resonators with clamped edges and studying numerically their mechanical responses. Both static and dynamic responses are treated, and we find good agreement with recent experimental findings.

Determination of the Bending Rigidity of Graphene via Electrostatic Actuation of Buckled Membranes

Classical continuum mechanics is used extensively to predict the properties of nanoscale materials such as graphene. The bending rigidity, κ, is an important parameter that is used, for example, to predict the performance of graphene nanoelectromechanical devices and also ripple formation. Despite its importance, there is a large spread in the theoretical predictions of κ for few-layer graphene. We have used the snap-through behavior of convex buckled graphene membranes under the application of electrostatic pressure to determine experimentally values of κ for double-layer graphene membranes. We demonstrate how to prepare convex-buckled suspended graphene ribbons and fully clamped suspended membranes and show how the determination of the curvature of the membranes and the critical snap-through voltage, using AFM, allows us to extract κ. The bending rigidity of bilayer graphene membranes under ambient conditions was determined to be 35.5−15.0 +20.0 eV. Monolayers are shown to have significantly lower κ than bilayers.

Nonlinear Damping in Graphene Resonators

Based on a continuum mechanical model for single-layer graphene, we propose and analyze a microscopic mechanism for dissipation in nanoelectromechanical graphene resonators. We find that coupling between flexural modes and in-plane phonons leads to linear and nonlinear damping of out-of-plane vibrations. By tuning external parameters such as bias and ac voltages, one can cross over from a linear-to a nonlinear-damping dominated regime. We discuss the behavior of the effective quality factor in this context. DOI: 10.1103/PhysRevB.86.235435

Electronic superlattices in corrugated graphene

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 wavelength. Transport through the ribbon depends sensitively 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 band edge energy, a strong current switching occurs as a function of an applied back gate 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 degree of freedom for graphene-based electronics.

Frequency tuning, nonlinearities and mode coupling in circular mechanical graphene resonators

We study circular nanomechanical graphene resonators by means of continuum elasticity theory, treating them as membranes. We derive dynamic equations for the flexural mode amplitudes. Due to the geometrical nonlinearity the mode dynamics can be modeled by coupled Duffing equations. By solving the Airy stress problem we obtain analytic expressions for the eigenfrequencies and nonlinear coefficients as functions of the radius, suspension height, initial tension, back-gate voltage and elastic constants, which we compare with finite element simulations. Using perturbation theory, we show that it is necessary to include the effects of the non-uniform stress distribution for finite deflections. This correctly reproduces the spectrum and frequency tuning of the resonator, including frequency crossings.

Nanomechanical mass measurement using nonlinear response of a graphene membrane

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.

Direct Transmission Detection of Tunable Mechanical Resonance in an Individual Carbon Nanofiber Relay

A direct on-chip transmission measurement of the resonance frequency of an individual singly clamped carbon nanofiber relay is reported. The experimental results are in good agreement with a small signal model and show the expected tuning of the resonance frequency with changing bias voltage.

Multiflavor bosonic Hubbard models in the first excited Bloch band of an optical lattice

We propose that by exciting ultracold atoms from the zeroth to the first Bloch band in an optical lattice, multiflavor bosonic Hubbard Hamiltonians can be realized in a different way. In these systems, each flavor hops in a separate direction and on-site exchange terms allow pairwise conversion between different flavors. Using band-structure calculations, we determine the parameters entering these Hamiltonians and derive the mean-field ground-state phase diagram for two effective Hamiltonians (two dimensional, two flavors, and three dimensional, three flavors). Further, we estimate the stability of atoms in the first band using second-order perturbation theory and find lifetimes that can be considerably (10\char21{}100 times) longer than the relevant time scale associated with intersite hopping dynamics, suggesting that quasiequilibrium can be achieved in these metastable states.

Nanomechanical displacement detection using coherent transport in graphene nanoribbon resonators

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 mechanical deformations couple. 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 similar to (w/L)(2) due to a deflection w leads to a relative change in conductance delta G/G similar to (w(2)/a(0)L), where a(0) approximate to 1.4 angstrom.

Energy-dependent path of dissipation in nanomechanical resonators

Energy decay plays a central role in a wide range of phenomena, such as optical emission, nuclear fission, and dissipation in quantum systems. Energy decay is usually described as a system leaking energy irreversibly into an environmental bath. Here, we report on energy decay measurements in nanomechanical systems based on multilayer graphene that cannot be explained by the paradigm of a system directly coupled to a bath. As the energy of a vibrational mode freely decays, the rate of energy decay changes abruptly to a lower value. This finding can be explained by a model where the measured mode hybridizes with other modes of the resonator at high energy. Below a threshold energy, modes are decoupled, resulting in comparatively low decay rates and giant quality factors exceeding 1 million. Our work opens up new possibilities to manipulate vibrational states, engineer hybrid states with mechanical modes at completely different frequencies, and to study the collective motion of this highly tunable system.