Nanoelectromechanical systems were fabricated from single- and multilayer graphene sheets by mechanically exfoliating thin sheets from graphite over trenches in silicon oxide. Vibrations with fundamental resonant frequencies in the megahertz range are actuated either optically or electrically and detected optically by interferometry. We demonstrate room-temperature charge sensitivities down to 8 x 10(-4) electrons per root hertz. The thinnest resonator consists of a single suspended layer of atoms and represents the ultimate limit of two-dimensional nanoelectromechanical systems.

We demonstrate that a monolayer graphene membrane is impermeable to standard gases including helium. By applying a pressure difference across the membrane, we measure both the elastic constants and the mass of a single layer of graphene. This pressurized graphene membrane is the world's thinnest balloon and provides a unique separation barrier between 2 distinct regions that is only one atom thick.Membranes are fundamental components of a wide variety of physical, chemical, and biological systems, used in everything from cellular compartmentalization to mechanical pressure sensing. They divide space into two regions, each capable of possessing different physical or chemical properties. A simple example is the stretched surface of a balloon, where a pressure difference across the balloon is balanced by the surface tension in the membrane. Graphene, a single layer of graphite, is the ultimate limit: a chemically stable and electrically conducting membrane one atom in thickness. 1-3 An interesting question is whether such an atomic membrane can be impermeable to atoms, molecules and ions. In this letter, we address this question for gases. We show that these membranes are impermeable and can support pressure differences larger than one atmosphere. We use such pressure differences to tune the mechanical resonance frequency by ∼100 MHz. This allows us to measure the mass and elastic constants of graphene membranes. We demonstrate that atomic layers of graphene have stiffness similar to bulk graphite (E ∼ 1 TPa). These results show that single atomic sheets can be integrated with microfabricated structures to create a new class of atomic scale membrane-based devices.A schematic of the device geometry used heresa graphene-sealed microchambersis shown in Figure 1a. Graphene sheets are suspended over predefined wells in silicon oxide using mechanical exfoliation (see Supporting Information). Each graphene membrane is clamped on all sides by the van der Waals force between the graphene and SiO 2 , creating a ∼(µm) 3 volume of confined gas. The inset of Figure 1a shows an optical image of a single layer graphene sheet forming a sealed square drumhead with a width W ) 4.75 µm on each side. Raman spectroscopy was used to confirm that this graphene sheet was a single layer in thickness. [4][5][6] Chambers with graphene thickness from 1 to ∼75 layers were studied.After initial fabrication, the pressure inside the microchamber, p int , is atmospheric pressure (101 kPa). If the pressure external to the chamber, p ext , is changed, we found that p int will equilibrate to p ext on a time scale that ranges from minutes to days, depending on the gas species and the temperature. On shorter time scales than this equilibration time, a significant pressure difference ∆p ) p int -p ext can exist across the membrane, causing it to stretch like the surface of a balloon (Figure 1b). Examples are shown for ∆p > 0 in Figure 1c and ∆p < 0 in Figure 1d.To create a positive pressure difference, ∆p > 0, as shown in Figure 1c, we place a s...

Quality factors as high as 207 000 are demonstrated at room temperature for radio-frequency silicon nitride string resonators with cross sectional dimensions on the scale of 100nm, made with a nonlithographic technique. A product of quality factor and surface to volume ratio greater than 6000nm−1 is presented, the highest yet reported. Doubly clamped nanostring resonators are fabricated in high tensile-stress silicon nitride using a nonlithographic electrospinning process. We fabricate devices with an electron beam process, and demonstrate frequency and quality factor results identical to those obtained with the nonlithographic technique. We also compare high tensile-stress doubly clamped beams with doubly clamped and cantilever resonators made of a lower stress material, as well as cantilever beams made of the high stress material. In all cases, the doubly clamped high stress beams have the highest quality factors. We therefore attribute the high quality factors to high tensile stress. Potential dominant loss mechanisms are discussed, including surface and clamping losses, and thermoelastic dissipation. Some practical advantages offered by these nanostrings for mass sensing are discussed.

Graphene's unparalleled strength, stiffness, and low mass per unit area make it an ideal material for nanomechanical resonators, but its relatively low quality factor is an important drawback that has been difficult to overcome. Here, we use a simple procedure to fabricate circular mechanical resonators of various diameters from graphene grown by chemical vapor deposition. In addition to highly reproducible resonance frequencies and mode shapes, we observe a striking improvement of the membrane quality factor with increasing size. At room temperature, we observe quality factors as high as 2400 ± 300 for a resonator 22.5 μm in diameter, about an order of magnitude greater than previously observed quality factors for monolayer graphene. Measurements of quality factor as a function of modal frequency reveal little dependence of Q on frequency. These measurements shed light on the mechanisms behind dissipation in monolayer graphene resonators and demonstrate that the quality factor of graphene resonators relative to their thickness is among the highest of any mechanical resonator demonstrated to date.

By virtue of their low mass and stiffness, atomically thin mechanical resonators are attractive candidates for use in optomechanics. Here, we demonstrate photothermal back-action in a graphene mechanical resonator comprising one end of a Fabry-Perot cavity. As a demonstration of the utility of this effect, we show that a continuous wave laser can be used to cool a graphene vibrational mode or to power a graphene-based tunable frequency oscillator. Owing to graphene's high thermal conductivity and optical absorption, photothermal optomechanics is efficient in graphene and could ultimately enable laser cooling to the quantum ground state or applications such as photonic signal processing.

We fabricated large arrays of suspended, single-layer graphene membrane resonators using chemical vapor deposition (CVD) growth followed by patterning and transfer. We measure the resonators using both optical and electrical actuation and detection techniques. We find that the resonators can be modeled as flat membranes under tension, and that clamping the membranes on all sides improves agreement with our model and reduces the variation in frequency between identical resonators. The resonance frequency is tunable with both electrostatic gate voltage and temperature, and quality factors improve dramatically with cooling, reaching values up to 9000 at 10 K. These measurements show that it is possible to produce large arrays of CVD-grown graphene resonators with reproducible properties and the same excellent electrical and mechanical properties previously reported for exfoliated graphene.

We report measurements of the superfluid density and transition temperature of 'He confined within 98.2% open aerogel. Both the superAuid fraction and the temperature at which the superf1uid is manifested are suppressed strongly from their bulk values. The results suggest that the aerogel reduces the order parameter by a mechanism other than as a diffusely scattering surface. PACS numbers: 67.57.Pq, 47.55.Mh, 67.57.De In 4He the nature of aerogels as a quenched impurity has been shown to exert a profound effect on the character of the superfluid phase transition [1]. Recent results on He-He mixtures reveal a striking modification of the phase diagram of helium mixtures in aerogel [2], indicating the possible coexistence of 4He and 3He superfluids. In order to explore this possibility, we undertook a study of pure 3He in aerogel. In this paper we report on the behavior of pure 3He confined in 98.2% open silica aerogel. Aerogels are very dilute networks of randomly interconnected thin strands of silica [3]. The typical strand diameter is thought to be on the order of 50 A. Small angle x-ray scattering experiments together with vapor pressure measurements have been interpreted as showing a broad distribution of strand separations ranging from 25 to nearly 1000 A [4 -6). The open geometry together with the small diameter of the strands make aerogel distinct from other substrates or materials for the study of the confinement of He. To explore superfiuidity of pure He in this medium we constructed a torsion pendulum (resonant frequency -943 Hz) containing 0.29 cm3 of 98.2% open aerogel. The 3He used was purified to reduce the 4He content to below 10 ppm, which corresponds to less than 0.001 monolayer. Since the viscous penetration depth 6 in 3He is so large compared with the strand spacing (6 -300 p, m at 2 mK), all the normal fluid is coupled to the oscillator. Experiments with pure 4He in this cell show that only 1% of the fully developed He superfiuid was not decoupled from the oscillator. The superAuid density p, is proportional to the period shift AP below the superfiuid transition. In order to avoid any pressure dependences of the torsion constant, the sensitivity of the oscillator was calibrated using the fill signal at 0 bar, which gives p, = 0.071 g/cm3 p, s /t. P. The superfluid fraction at each pressure, p, /p, is obtained by dividing p, by the total density of the bulk fiuid at each pressure. Signal from bulk He was minimal since open volumes had been eliminated by growing the aerogel directly into the oscillator. A lanthanum diluted cerous magnesium ac susceptibility thermometer, calibrated against the melting curve [7], was used for thermometry. tn CV o &õ o o o o D 0.5 1.0 1.5 2,0 Temperature (mK) 2.5 FIG. 1. The superfluid fraction, p, /p, at various pressures as a function of temperature. The curves correspond to, from left to right, 3.4, 4.0, 5.0, 6.1, 7.0, 8.5, 10, 13, 15, 20, 25, and 29 bars. The inset shows p, /p in the bulk for 0, 5, 10, 15, and 20 bars over the same temperature range.The super...

We present data on nanofabricated suspended silicon wires driven at resonance. The wires are electrostatically driven and detected optically. We have observed wires with widths as small as 45 nm and resonant frequencies as high as 380 MHz. We see a strong dependence of the resonant quality factor on the surface to volume ratio.