Daniel Midtvedt

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.

A pH-driven transition of the cytoplasm from a fluid- to a solid-like state promotes entry into dormancy

Cells can enter into a dormant state when faced with unfavorable conditions. However, how cells enter into and recover from this state is still poorly understood. Here, we study dormancy in different eukaryotic organisms and find it to be associated with a significant decrease in the mobility of organelles and foreign tracer particles. We show that this reduced mobility is caused by an influx of protons and a marked acidification of the cytoplasm, which leads to widespread macromolecular assembly of proteins and triggers a transition of the cytoplasm to a solid-like state with increased mechanical stability. We further demonstrate that this transition is required for cellular survival under conditions of starvation. Our findings have broad implications for understanding alternative physiological states, such as quiescence and dormancy, and create a new view of the cytoplasm as an adaptable fluid that can reversibly transition into a protective solid-like state. DOI: http://dx.doi.org/10.7554/eLife.09347.001

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

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.

Carbon Nanotube Field Effect Transistors with Suspended Graphene Gates

Novel field effect transistors with suspended graphene gates are demonstrated. By incorporating mechanical motion of the gate electrode, it is possible to improve the switching characteristics compared to a static gate, as shown by a combination of experimental measurements and numerical simulations. The mechanical motion of the graphene gate is confirmed by using atomic force microscopy to directly measure the electrostatic deflection. The device geometry investigated here can also provide a sensitive measurement technique for detecting high-frequency motion of suspended membranes as required, e.g., for mass sensing.

Fermi-Pasta-Ulam Physics with Nanomechanical Graphene Resonators: Intrinsic Relaxation and Thermalization from Flexural Mode Coupling

Thermalization in nonlinear systems is a central concept in statistical mechanics and has been extensively studied theoretically since the seminal work of Fermi, Pasta, and Ulam. Using molecular dynamics and continuum modeling of a ring-down setup, we show that thermalization due to nonlinear mode coupling intrinsically limits the quality factor of nanomechanical graphene drums and turns them into potential test beds for Fermi-Pasta-Ulam physics. We find the thermalization rate Γ to be independent of radius and scaling as Γ∼T*/εpre2, where T* and εpre are effective resonator temperature and prestrain.

Strain–displacement relations for strain engineering in single-layer 2d materials

We investigate the electromechanical coupling in single-layer 2d materials. For non-Bravais lattices, we find important corrections to the standard macroscopic strain-microscopic atomic-displacement theory. We put forward a general and systematic approach to calculate strain-displacement relations for several classes of 2d materials. We apply our findings to graphene as a study case, by combining a tight binding and a valence force-field model to calculate electronic and mechanical properties of graphene nanoribbons under strain. The results show good agreement with the predictions of the Dirac equation coupled to continuum mechanics. For this long wave-limit effective theory, we find that the strain-displacement relations lead to a renormalization correction to the strain-induced pseudo-magnetic fields. A similar renormalization is found for the strain-induced band-gap of black phosphorous. Implications for nanomechanical properties and electromechanical coupling in 2d materials are discussed.

Nonlinear phononics using atomically thin membranes

Phononic crystals and acoustic metamaterials are used to tailor phonon and sound propagation properties by utilizing artificial, periodic structures. Analogous to photonic crystals, phononic band gaps can be created, which influence wave propagation and, more generally, allow engineering of the acoustic properties of a system. Beyond that, nonlinear phenomena in periodic structures have been extensively studied in photonic crystals and atomic Bose-Einstein condensates in optical lattices. However, creating nonlinear phononic crystals or nonlinear acoustic metamaterials remains challenging and only few examples have been demonstrated. Here, we show that atomically thin and periodically pinned membranes support coupled localized modes with nonlinear dynamics. The proposed system provides a platform for investigating nonlinear phononics.

The Matrix protein M1 from influenza C virus induces tubular membrane invaginations in an in vitro cell membrane model.

Matrix proteins from enveloped viruses play an important role in budding and stabilizing virus particles. In order to assess the role of the matrix protein M1 from influenza C virus (M1-C) in plasma membrane deformation, we have combined structural and in vitro reconstitution experiments with model membranes. We present the crystal structure of the N-terminal domain of M1-C and show by Small Angle X-Ray Scattering analysis that full-length M1-C folds into an elongated structure that associates laterally into ring-like or filamentous polymers. Using negatively charged giant unilamellar vesicles (GUVs), we demonstrate that M1-C full-length binds to and induces inward budding of membrane tubules with diameters that resemble the diameter of viruses. Membrane tubule formation requires the C-terminal domain of M1-C, corroborating its essential role for M1-C polymerization. Our results indicate that M1-C assembly on membranes constitutes the driving force for budding and suggest that M1-C plays a key role in facilitating viral egress.

Strain-tuning of vacancy-induced magnetism in graphene nanoribbons

Vacancies in graphene lead to the appearance of localized electronic states with non-vanishing spin moments. Using a mean-field Hubbard model and an effective double-quantum dot description we investigate the influence of strain on localization and magnetic properties of the vacancy-induced states in semiconducting armchair nanoribbons. We find that the exchange splitting of a single vacancy and the singlet-triplet splitting for two vacancies can be widely tuned by applying uniaxial strain, which is crucial for spintronic applications.