Jari M. Kinaret

Science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems

We present the science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems, targeting an evolution in technology, that might lead to impacts and benefits reaching into most areas of society. This roadmap was developed within the framework of the European Graphene Flagship and outlines the main targets and research areas as best understood at the start of this ambitious project. We provide an overview of the key aspects of graphene and related materials (GRMs), ranging from fundamental research challenges to a variety of applications in a large number of sectors, highlighting the steps necessary to take GRMs from a state of raw potential to a point where they might revolutionize multiple industries. We also define an extensive list of acronyms in an effort to standardize the nomenclature in this emerging field.

A CARBON-NANOTUBE-BASED NANORELAY

We investigate the operational characteristics of a nanorelay based on a conducting carbon nanotube placed on a terrace in a silicon substrate. The nanorelay is a three-terminal device that acts as a switch in the gigahertz regime. Potential applications include logic devices, memory elements, pulse generators, and current or voltage amplifiers.

Coupling Mechanics to Charge Transport in Carbon Nanotube Mechanical Resonators

Tuning Carbon Nanotube Resonances Nanoscale resonators can be used in sensing and for processing mechanical signals. Single-walled carbon nanotubes have potential design advantages as resonators in that their oscillatory motion could be coupled to electron transport (see the Perspective by Hone and Deshpande). Steele et al. (p. 1103, published online 23 July) and Lassagne et al. (p. 1107, published online 23 July) report that the resonance frequency of a suspended single-walled carbon nanotube can be excited when operated as a single-electron transistor at low temperatures. Electrostatic forces are set up when the carbon nanotubes charge and discharge. The resonance frequency depends on applied voltages, and the coupling is strong enough to drive the mechanical motion into the nonlinear response regime. Differences in the responses of the devices in the two studies reflect in part the different quality factors of the resonators and different cryogenic temperatures. Individual electrons tunneling onto and out of a carbon nanotube can be used to tune its oscillatory motion. Nanoelectromechanical resonators have potential applications in sensing, cooling, and mechanical signal processing. An important parameter in these systems is the strength of coupling the resonator motion to charge transport through the device. We investigated the mechanical oscillations of a suspended single-walled carbon nanotube that also acts as a single-electron transistor. The coupling of the mechanical and the charge degrees of freedom is strikingly strong as well as widely tunable (the associated damping rate is ~3 × 106 Hz). In particular, the coupling is strong enough to drive the oscillations in the nonlinear regime.

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.

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

High frequency properties of a CNT-based nanorelay

We have theoretically investigated the high frequency properties of a carbon-nanotube-based three-terminal nanoelectromechanical relay. The intrinsic mechanical frequency of the relay is in the GHz regime, and the electromechanical coupling shows a non-linear resonant behaviour in this frequency range. We discuss how these resonances may be detected and show that the resonance frequencies can be tuned by the bias voltage. Also, we show that the influence of external electromagnetic fields on the relay is negligible at all frequencies.

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.

Effects of surface forces and phonon dissipation in a three-terminal nanorelay

We have performed a theoretical analysis of the operational characteristics of a carbon–nanotube-based three-terminal nanorelay. We show that short range and van der Waals forces have a significant impact on the characteristics of the relay and introduce design constraints. We also investigate the effects of dissipation due to phonon excitation in the drain contact, which changes the switching time scales of the system, decreasing the longest time scale by 2 orders of magnitude. We show that the nanorelay can be used as a memory element and investigate the dynamics and properties of such a device.

LINEAR-RESPONSE THEORY OF COULOMB DRAG IN COUPLED ELECTRON SYSTEMS

We report a fully microscopic theory for transconductivity, or, equivalently, momentum transfer rate, of Coulomb coupled electron systems. We use the Kubo linear-response formalism, and our main formal result expresses the transconductivity in terms of two fluctuation diagrams, which are topologically related, but not equivalent to, the Aslamazov-Larkin diagrams known from superconductivity. Results reported elsewhere are shown to be special cases of our general expression; specifically, we recover the Boltzmann equation result in the semiclassical clean limit, and the memory function results for dirty systems with constant impurity scattering rates. Furthermore, we show that for energy-dependent relaxation times, the final result is not expressible in terms of standard density-response functions. Other results include (i) at T=0, the frequency dependence of the transfer rate is found to be proportional to \ensuremath{\Omega} and

Nanomechanical mass measurement using nonlinear response of a graphene membrane

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