Observation of suppressed viscosity in the normal state of 3He due to superfluid fluctuations.

Evidence of fluctuations in transport have long been predicted in 3He. They are expected to contribute only within 100µK of Tc and play a vital role in the theoretical modeling of ordering; they encode details about the Fermi liquid parameters, pairing symmetry, and scattering phase shifts. It is expected that they will be of crucial importance for transport probes of the topologically nontrivial features of superfluid 3He under strong confinement. Here we characterize the temperature and pressure dependence of the fluctuation signature, by monitoring the quality factor of a quartz tuning fork oscillator. We have observed a fluctuation-driven reduction in the viscosity of bulk 3He, finding data collapse consistent with the predicted theoretical behavior.

Path-Dependent Supercooling of the

We examine the discontinuous first-order superfluid ^{3}He A to B transition in the vicinity of the polycritical point (2.232 mK and 21.22 bar). We find path-dependent transitions: cooling at fixed pressure yields a well-defined transition line in the temperature-pressure plane, but this line can be reliably crossed by depressurizing at nearly constant temperature after transiting T_{c} at a higher pressure. This path dependence is not consistent with any of the standard B-phase nucleation mechanisms in the literature. This symmetry breaking transition is a potential simulator for first order transitions in the early Universe.

Evidence for a Spatially Modulated Superfluid Phase of

In superfluid ^{3}He-B confined in a slab geometry, domain walls between regions of different order parameter orientation are predicted to be energetically stable. Formation of the spatially modulated superfluid stripe phase has been proposed. We confined ^{3}He in a 1.1 µm high microfluidic cavity and cooled it into the B phase at low pressure, where the stripe phase is predicted. We measured the surface-induced order parameter distortion with NMR, sensitive to the formation of domains. The results rule out the stripe phase, but are consistent with 2D modulated superfluid order.

Measuring Frequency Fluctuations in Nonlinear Nanomechanical Resonators.

Advances in nanomechanics within recent years have demonstrated an always expanding range of devices, from top-down structures to appealing bottom-up MoS2 and graphene membranes, used for both sensing and component-oriented applications. One of the main concerns in all of these devices is frequency noise, which ultimately limits their applicability. This issue has attracted a lot of attention recently, and the origin of this noise remains elusive to date. In this article we present a very simple technique to measure frequency noise in nonlinear mechanical devices, based on the presence of bistability. It is illustrated on silicon-nitride high-stress doubly clamped beams, in a cryogenic environment. We report on the same T/ f dependence of the frequency noise power spectra as reported in the literature. But we also find unexpected damping fluctuations, amplified in the vicinity of the bifurcation points; this effect is clearly distinct from already reported nonlinear dephasing and poses a fundamental limit on the measurement of bifurcation frequencies. The technique is further applied to the measurement of frequency noise as a function of mode number, within the same device. The relative frequency noise for the fundamental flexure δ f/ f0 lies in the range 0.5-0.01 ppm (consistent with the literature for cryogenic MHz devices) and decreases with mode number in the range studied. The technique can be applied to any type of nanomechanical structure, enabling progress toward the understanding of intrinsic sources of noise in these devices.

Low-Power Photothermal Self-Oscillation of Bimetallic Nanowires.

We investigate the nonlinear mechanics of a bimetallic, optically absorbing SiN-Nb nanowire in the presence of incident laser light and a reflecting Si mirror. Situated in a standing wave of optical intensity and subject to photothermal forces, the nanowire undergoes self-induced oscillations at low incident light thresholds of <1 µW due to engineered strong temperature-position (T-z) coupling. Along with inducing self-oscillation, laser light causes large changes to the mechanical resonant frequency ω0 and equilibrium position z0 that cannot be neglected. We present experimental results and a theoretical model for the motion under laser illumination. In the model, we solve the governing nonlinear differential equations by perturbative means to show that self-oscillation amplitude is set by the competing effects of direct T-z coupling and 2ω0 parametric excitation due to T-ω0 coupling. We then study the linearized equations of motion to show that the optimal thermal time constant τ for photothermal feedback is τ → ∞ rather than the previously reported ω0 τ = 1. Lastly, we demonstrate photothermal quality factor (Q) enhancement of driven motion as a means to counteract air damping. Understanding photothermal effects on nano- and micromechanical devices, as well as nonlinear aspects of optics-based motion detection, can enable new device applications as oscillators or other electronic elements with smaller device footprints and less stringent ambient vacuum requirements.

Graphene metallization of high-stress silicon nitride resonators for electrical integration.

High stress stoichiometric silicon nitride resonators, whose quality factors exceed one million, have shown promise for applications in sensing, signal processing, and optomechanics. Yet, electrical integration of the insulating silicon nitride resonators has been challenging, as depositing even a thin layer of metal degrades the quality factor significantly. In this work, we show that graphene used as a conductive coating for Si3N4 membranes reduces the quality factor by less than 30% on average, which is minimal when compared to the effect of conventional metallization layers such as chromium or aluminum. The electrical integration of Si3N4-Graphene (SiNG) heterostructure resonators is demonstrated with electrical readout and electrostatic tuning of the frequency by up to 0.3% per volt. These studies demonstrate the feasibility of hybrid graphene/nitride mechanical resonators in which the electrical properties of graphene are combined with the superior mechanical performance of silicon nitride.

Control of the graphene-protein interface is required to preserve adsorbed protein function.

Graphene's suite of useful properties makes it of interest for use in biosensors. However, graphene interacts strongly with hydrophobic components of biomolecules, potentially altering their conformation and disrupting their biological activity. We have immobilized the protein Concanavalin A onto a self-assembled monolayer of multivalent tripodal molecules on single-layer graphene. We used a quartz crystal microbalance (QCM) to show that tripod-bound Concanavalin A retains its affinity for polysaccharides containing α-D-glucopyrannosyl groups as well as for the α-D-mannopyranosyl groups located on the cell wall of Bacillus subtilis. QCM measurements on unfunctionalized graphene indicate that adsorption of Concanavalin A onto graphene is accompanied by near-complete loss of these functions, suggesting that interactions with the graphene surface induce deleterious structural changes to the protein. Given that Concanavalin A's tertiary structure is thought to be relatively robust, these results suggest that other proteins might also be denatured upon adsorption onto graphene, such that the graphene-biomolecule interface must be considered carefully. Multivalent tripodal binding groups address this challenge by anchoring proteins without loss of function and without disrupting graphene's desirable electronic structure.

Surface-induced order parameter distortion in superfluid ³He-B measured by nonlinear NMR.

The B phase of superfluid 3He is a three-dimensional time-reversal invariant topological superfluid, predicted to support gapless Majorana surface states. We confine superfluid 3He into a thin nanofluidic slab geometry. In the presence of a weak symmetry-breaking magnetic field, we have observed two possible states of the confined 3He-B phase manifold, through the small tipping angle NMR response. Large tipping angle nonlinear NMR has allowed the identification of the order parameter of these states and enabled a measurement of the surface-induced gap distortion. The results for two different quasiparticle surface scattering boundary conditions are compared with the predictions of weak-coupling quasiclassical theory. We identify a textural domain wall between the two B phase states, the edge of which at the cavity surface is predicted to host gapless states, protected in the magnetic field.

Photothermal self-oscillation and laser cooling of graphene optomechanical systems.

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.

High, size-dependent quality factor in an array of graphene mechanical resonators.

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.

Large-scale arrays of single-layer graphene resonators.

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.

Strong gate coupling of high-Q nanomechanical resonators.

The detection of mechanical vibrations near the quantum limit is a formidable challenge since the displacement becomes vanishingly small when the number of phonon quanta tends toward zero. An interesting setup for on-chip nanomechanical resonators is that of coupling them to electrical microwave cavities for detection and manipulation. Here we show how to achieve a large cavity coupling energy of up to (2π) 1 MHz/nm for metallic beam resonators at tens of megahertz. We used focused ion beam (FIB) cutting to produce uniform slits down to 10 nm, separating patterned resonators from their gate electrodes, in suspended aluminum films. We measured the thermomechanical vibrations down to a temperature of 25 mK, and we obtained a low number of about 20 phonons at the equilibrium bath temperature. The mechanical properties of Al were excellent after FIB cutting, and we recorded a quality factor of Q ∼ 3 × 10(5) for a 67 MHz resonator at a temperature of 25 mK. Between 0.2 and 2 K we find that the dissipation is linearly proportional to the temperature.

Fabrication of a nanomechanical mass sensor containing a nanofluidic channel.

Nanomechanical resonators operating in vacuum are capable of detecting and weighing single biomolecules, but their application to the life sciences has been limited by viscous forces that impede their motion in liquid environments. A promising approach to avoid this problem, encapsulating the fluid within a mechanical resonator surrounded by vacuum, has not yet been tried with resonant sensors of mass less than approximately 100 ng, despite predictions that devices with smaller effective mass will have proportionally finer mass resolution. Here, we fabricate and evaluate the performance of doubly clamped beam resonators that contain filled nanofluidic channels and have masses of less than 100 pg. These nanochannel resonators operate at frequencies on the order of 25 MHz and when filled with fluid have quality factors as high as 800, 2 orders of magnitude higher than that of resonators of comparable size and frequency operating in fluid. Fluid density measurements reveal a mass responsivity of 100 Hz/fg and a noise equivalent mass of 2 fg. Our analysis suggests that realistic improvements in the quality factor and frequency stability of nanochannel resonators would render these devices capable of sensing attogram masses from liquid.

Free-standing epitaxial graphene.

We report on a method to produce free-standing graphene sheets from epitaxial graphene on silicon carbide (SiC) substrate. Doubly clamped nanomechanical resonators with lengths up to 20 microm were patterned using this technique and their resonant motion was actuated and detected optically. Resonance frequencies of the order of tens of megahertz were measured for most devices, indicating that the resonators are much stiffer than expected for beams under no tension. Raman spectroscopy suggests that the graphene is not chemically modified during the release of the devices, demonstrating that the technique is a robust means of fabricating large-area suspended graphene structures.

Impermeable atomic membranes from graphene sheets.

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.

Macroscopic tuning of nanomechanics: substrate bending for reversible control of frequency and quality factor of nanostring resonators.

We have employed a chip-bending method to exert continuous and reversible control over the tensile stress in doubly clamped nanomechanical beam resonators. Tensile stress is shown to increase the quality factor of both silicon nitride and single-crystal silicon resonators, implying that added tension can be used as a general, material-independent route to increased quality factor. With this direct stretching technique, we demonstrate beam resonators with unprecedented tunability of both frequency and quality factor. Devices can be tuned back and forth between a high and low stress state, with frequency tunability as large as several hundred percent demonstrated. Over this wide range of frequency, quality factor is also tuned by as much as several hundred percent, providing insights into the loss mechanisms in these materials and this class of nanoresonator. Devices with frequencies in the 1-100 MHz range are studied, with quality factor as high as 390,000 achieved at room temperature, for a silicon nitride device with cross-sectional dimensions below 1 microm, operating in a high stress state. This direct stretching technique may prove useful for the identification of loss mechanisms that contribute to the energy balance in nanomechanical resonators, allowing for the development of new designs that would display higher quality factors. Such devices would have the ability to resolve smaller addendum masses and thus allow more sensitive detection and offer the potential for providing access to previously inaccessible dissipation regimes at low temperatures. This technique provides the ability to dramatically tune both frequency and quality factor, enabling future mechanical resonators to be used as variable frequency references as well as variable band-pass filters in signal-processing applications.

Electromechanical resonators from graphene sheets.

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.

Optically driven resonance of nanoscale flexural oscillators in liquid.

We demonstrate the operation of radio frequency nanoscale flexural resonators in air and liquid. Doubly clamped string, as well as singly clamped cantilever resonators, with nanoscale cross-sectional dimensions and resonant frequencies as high as 145 MHz are driven in air as well as liquid with an amplitude modulated laser. We show that this laser drive technique can impart sufficient energy to a nanoscale resonator to overcome the strong viscous damping present in these media, resulting in a mechanical resonance that can be measured by optical interference techniques. Resonance in air, isopropyl alcohol, acetone, water, and phosphate-buffered saline is demonstrated for devices having cross-sectional dimensions close to 100 nm. For operation in air, quality factors as high as 400 at 145 MHz are demonstrated. In liquid, quality factors ranging from 3 to 10 and frequencies ranging from 20 to 100 MHz are observed. These devices, and an all-optical actuation and detection system, may provide insight into the physics of the interaction of nanoscale mechanical structures with their environments, greatly extending the viscosity range over which such small flexural resonant devices can be operated.