Graphene mechanical oscillators with tunable frequency

High-quality-factor viscoelastic nanomechanical resonators from moiré superlattices

The moiré superlattice, created by stacking van der Waals layered materials with rotational misalignments, exhibits a multitude of emergent correlated phenomena ranging from superconductivity to Mott insulating states. In addition to exotic electronic states, the intricate networks of incommensurate lattices may give rise to polymer-like viscoelasticity, which combines the properties of both elastic solids and viscous fluids. This phenomenon may enrich the dynamics of nanomechanical resonators, in which viscoelasticity has not played a role thus far. Here, we report on a controllable hysteretic response of the nanomechanical vibrations in twisted bilayer graphene membranes, which we attribute to viscoelasticity. Accompanying this hysteretic response, we measure unusually large mechanical quality factors Q reaching a remarkably high value of  ~1900 at room temperature. We interpret the enhancement of Q as a signature of dissipation dilution, a phenomenon of considerable interest that has recently been harnessed in quantum optomechanical systems. Viscoelasticity features a "lossless" potential that overcomes the corrugation registry and reinforces such a dissipation dilution. Our work introduces the moiré superlattice as a promising system for viscoelasticity engineering through rotating angles and for observing emergent nanoelectromechanical couplings.

Nanomechanical Characterization of an Antiferromagnetic Topological Insulator

The antiferromagnetic topological insulator MnBi2Te4 (MBT) exhibits an ideal platform for investigating unique topological and magnetic properties. While the transport characteristics of magnetic phase transitions in the MBT materials have been extensively studied, the understanding of their mechanical properties and magneto-mechanical coupling remains limited. Here, we utilize nanoelectromechanical systems to probe the intrinsic magnetism in MBT thin flakes through magnetostrictive coupling. By analyzing the mechanical resonance signatures, we explore the magnetic phase transitions from antiferromagnetic (AFM) to canted antiferromagnetic (CAFM) to ferromagnetic (FM) phases as a function of magnetic field. Our results reveal the spin-flop transitions in MBT, characterized by frequency shifts in the mechanical resonance. To establish a correlation between the frequency shifts and the spin-canting states, we employ a magnetostrictive model to extract the magnetostrictive coefficients. Our study demonstrates a valuable approach using nanoelectromechanical systems to investigate magnetic phase transitions, magnetization, and magnetoelastic properties in antiferromagnetic topological insulators.

Dynamic tuning of terahertz atomic lattice vibration via cross-scale mode coupling to nanomechanical resonance in WSe2 membranes

Nanoelectromechanical systems (NEMS) based on atomically-thin tungsten diselenide (WSe2), benefiting from the excellent material properties and the mechanical degree of freedom, offer an ideal platform for studying and exploiting dynamic strain engineering and cross-scale vibration coupling in two-dimensional (2D) crystals. However, such opportunity has remained largely unexplored for WSe2 NEMS, impeding exploration of exquisite physical processes and realization of novel device functions. Here, we demonstrate dynamic coupling between atomic lattice vibration and nanomechanical resonances in few-layer WSe2 NEMS. Using a custom-built setup capable of simultaneously detecting Raman and motional signals, we accomplish cross-scale mode coupling between the THz crystal phonon and MHz structural vibration, achieving GHz frequency tuning in the atomic lattice modes with a dynamic gauge factor of 61.9, the best among all 2D crystals reported to date. Our findings show that such 2D NEMS offer great promises for exploring cross-scale physics in atomically-thin semiconductors.

Unveiling the tradeoff between device scale and surface nonidealities for an optimized quality factor at room temperature in 2D MoS2 nanomechanical resonators

A high quality (Q) factor is essential for enhancing the performance of resonant nanoelectromechanical systems (NEMS). NEMS resonators based on two-dimensional (2D) materials such as molybdenum disulfide (MoS2) have high frequency tunability, large dynamic range, and high sensitivity, yet room-temperature Q factors are typically less than 1000. Here, we systematically investigate the effects of device size and surface nonidealities on Q factor by measuring 52 dry-transferred fully clamped circular MoS2 NEMS resonators with diameters ranging from 1 μm to 8 μm, and optimize the Q factor by combining these effects with the strain-modulated dissipation model. We find that Q factor first increases and then decreases with diameter, with an optimized room-temperature Q factor up to 3315 ± 115 for a 2-μm-diameter device. Through extensive characterization and analysis using Raman spectroscopy, atomic force microscopy, and scanning electron microscopy, we demonstrate that surface nonidealities such as wrinkles, residues, and bubbles are especially significant for decreasing Q factor, especially for larger suspended membranes, while resonators with flat and smooth surfaces typically have larger Q factors. To further optimize Q factors, we measure and model Q factor dependence on the gate voltage, showing that smaller DC and radio-frequency (RF) driving voltages always lead to a higher Q factor, consistent with the strain-modulated dissipation model. This optimization of the Q factor delineates a straightforward and promising pathway for designing high-Q 2D NEMS resonators for ultrasensitive transducers, efficient RF communications, and low-power memory and computing.

Tunable Stochastic State Switching in 2D MoS2 Nanomechanical Resonators with Nonlinear Mode Coupling and Internal Resonance

Coupled nanomechanical resonators have unveiled fascinating physical phenomena, including phonon-cavity coupling, coupled energy decay pathway, avoided crossing, and internal resonance. Despite these discoveries, the mechanisms and control techniques of nonlinear mode coupling phenomena with internal resonances require further exploration. Here, we report on the observation of stochastic switching between the two resonance states with coupled 1:1 internal resonance, for resonant two-dimensional (2D) molybdenum disulfide (MoS2) nanoelectromechanical systems (NEMS), which is directly driven to the critical coupling regime without parametric pumping. We further demonstrate that the probability of state switching is linearly tunable from ∼0% to ∼100% by varying the driving voltage. Furthermore, we gradually increase the white noise amplitude and show that the probability of obtaining the higher-energy state decreases, and the stochastic switching phenomenon eventually disappears. The results provide insights into the dynamics of coupled NEMS resonators and open up new possibilities for sensing and stochastic computing.

Research on Fabrication of Phononic Crystal Soft-Supported Graphene Resonator

In aviation, aerospace, and other fields, nanomechanical resonators could offer excellent sensing performance. Among these, graphene resonators, as a new sensitive unit, are expected to offer very high mass and force sensitivity due to their extremely thin thickness. However, at present, the quality factor of graphene resonators at room temperature is generally low, which limits the performance improvement and further application of graphene resonators. Enhancing the quality factor of graphene resonators has emerged as a pressing research concern. In a previous study, we have proposed a new mechanism to reduce the energy dissipation of graphene resonators by utilizing phononic crystal soft-supported structures. We verified its feasibility through theoretical analysis and simulations. This article focuses on the fabrication of a phononic crystal soft-supported graphene resonator. In order to address the issues of easy fracture, deformation, and low success rate in the fabrication of phononic crystal soft-supported graphene resonators, we have studied key processes for graphene suspension release and focused ion beam etching. Through parameter optimization, finally, we have obtained phononic crystal soft-supported graphene resonators with varying cycles and pore sizes. Finally, we designed an optical excitation and detection platform based on Fabry-Pérot interference principle and explored the impact of laser power and spot size on phononic crystal soft-supported graphene resonators.

Flexible nanomechanical bit based on few-layer graphene

Mechanical computers have gained intense research interest at size scales ranging from nano to macro as they may complement electronic computers operating in extreme environments. While nanoscale mechanical computers may be easier to integrate with traditional electronic components, most current nanomechanical computers are based on volatile resonator systems that require continuous energy input. In this study, we propose a non-volatile nanomechanical bit based on the quasi-stable configurations of few-layer graphene with void defects, and demonstrate its multiple quasi-stable states by deriving an analytic relationship for the void configuration based on a competition between the bending energy and the cohesive energy. Using this nanomechanical bit, typical logic gates are constructed to perform Boolean calculations, including NOT, AND, OR, NAND and NOR gates, and demonstrate reprogrammability between these logic gates. We also study the accuracy and the stability of the nanomechanical bits based on the few-layer graphene. These findings provide a novel approach to realize the nanomechanical computing process.

Enhanced Polarization Properties of Holographic Storage Materials Based on RGO Size Effect

Polarized holographic properties play an important role in the holographic data storage of traditional organic recording materials. In this study, reduced graphene oxide (RGO) was introduced into a phenanthraquinone-doped polymethylmethacrylate (PQ/PMMA) photopolymer to effectively improve the orthogonal polarization holographic properties of the material. Importantly, the lateral size of RGO nanosheets has an important influence on the polymerization of MMA monomers. To some extent, a larger RGO diameter is more conducive to promoting the polymerization of MMA monomers and can induce more PMMA polymers to be grafted on its surface, thus obtaining a higher PMMA molecular weight. However, too large of a RGO will lead to too much grafting of the PMMA chain to shorten the length of a single PMMA chain, which will lead to the degradation of PQ/PMMA holographic performance. Compared with the original PQ/PMMA, the diffraction efficiency of the RGO-doped PQ/PMMA photopolymer can reach more than 11.4% (more than 3.5 times higher than the original PQ/PMMA), and its photosensitivity is significantly improved by 4.6 times. This study successfully synthesized RGO-doped PQ/PMMA high-performance photopolymer functional materials for multi-dimensional holographic storage by introducing RGO nanoparticles. Furthermore, the polarization holographic properties of PQ/PMMA photopolymer materials can be further accurately improved to a new level.

Achieving Ultrawide Tunability in Monolithically Fabricated Si Nanoresonator Devices

Nanoresonators are powerful and versatile tools promising to revolutionize a wide range of technological areas by delivering unparalleled performance in physical, chemical, biological sensing, signal and information processing, quantum computation, etc., via their high-frequency resonant vibration and rich dynamic behavior. Having the ability to tune the resonance frequency and dynamic behavior at the application stage promises further improvement in their effectiveness and enables novel applications. However, achieving significant room-temperature tunability in conventional (monolithically fabricated) nanoresonators is considered challenging. Here we demonstrate ultrawide electrostatic tuning (∼70%) of (initial) resonance-frequency (∼7% V-1) at room temperature in a monolithically fabricated ultrathin Si nanoresonator (width ∼ 40 nm, length ∼ 200 μm) device. Extreme electrostatic tuning of nonlinear behavior is also demonstrated by canceling the cubic-nonlinear coefficient and subsequently flipping its sign. Thus, these results are expected to provide remarkable operational flexibility and new capabilities to microfabricated resonators, which will benefit many technological areas.

Probing Linear to Nonlinear Damping in 2D Semiconductor Nanoelectromechanical Resonators toward a Unified Quality Factor Model

In resonant nanoelectromechanical systems (NEMS), the quality (Q) factor is essential for sensing, communication, and computing applications. While a large vibrational amplitude is useful for increasing the signal-to-noise ratio, the damping in this regime is more complex because both linear and nonlinear damping are important, and an accurate model for Q has not been fully explored. Here, we demonstrate that by combining the time-domain ringdown and frequency-domain resonance measurements, we extract the accurate Q for two-dimensional (2D) MoS2 and MoTe2 NEMS resonators at different vibration amplitudes. In particular, in the transition region between linear and nonlinear damping, Q can be precisely extracted by fitting to the ringdown characteristics. By varying AC driving, we tune the Q by ΔQ/Q = 269% and extract the nonlinear damping coefficient. We develop the dissipation model that well captures the linear to nonlinear damping, providing important insights for accurately modeling and optimizing Q in 2D NEMS resonators.

Negative cavity photon spectral function in an optomechanical system with two parametrically-driven mechanical modes

We propose an experimentally feasible optomechanical scheme to realize a negative cavity photon spectral function (CPSF) which is equivalent to a negative absorption. The system under consideration is an optomechanical system consisting of two mechanical (phononic) modes which are linearly coupled to a common cavity mode via the radiation pressure while parametrically driven through the coherent time-modulation of their spring coefficients. Using the equations of motion for the cavity retarded Green's function obtained in the framework of the generalized linear response theory, we show that in the red-detuned and weak-coupling regimes a frequency-dependent effective cavity damping rate (ECDR) corresponding to a negative CPSF can be realized by controlling the cooperativities and modulation parameters while the system still remains in the stable regime. Nevertheless, such a negativity which acts as an optomechanical gain never occurs in a standard (an unmodulated bare) cavity optomechanical system. Besides, we find that the presence of two modulated mechanical degrees of freedom provides more controllability over the magnitude and bandwidth of the negativity of CPSF, in comparison to the setup with a single modulated mechanical oscillator. Interestingly, the introduced negativity may open a new platform to realize an extraordinary (modified) optomechanically induced transparency (in which the input signal is amplified in the output) leading to a perfect tunable optomechanical filter with switchable bandwidth which can be used as an optical transistor.

Spin-mediated shear oscillators in a van der Waals antiferromagnet

Understanding how microscopic spin configuration gives rise to exotic properties at the macroscopic length scale has long been pursued in magnetic materials1-5. One seminal example is the Einstein-de Haas effect in ferromagnets1,6,7, in which angular momentum of spins can be converted into mechanical rotation of an entire object. However, for antiferromagnets without net magnetic moment, how spin ordering couples to macroscopic movement remains elusive. Here we observed a seesaw-like rotation of reciprocal lattice peaks of an antiferromagnetic nanolayer film, whose gigahertz structural resonance exhibits more than an order-of-magnitude amplification after cooling below the Néel temperature. Using a suite of ultrafast diffraction and microscopy techniques, we directly visualize this spin-driven rotation in reciprocal space at the nanoscale. This motion corresponds to interlayer shear in real space, in which individual micro-patches of the film behave as coherent oscillators that are phase-locked and shear along the same in-plane axis. Using time-resolved optical polarimetry, we further show that the enhanced mechanical response strongly correlates with ultrafast demagnetization, which releases elastic energy stored in local strain gradients to drive the oscillators. Our work not only offers the first microscopic view of spin-mediated mechanical motion of an antiferromagnet but it also identifies a new route towards realizing high-frequency resonators8,9 up to the millimetre band, so the capability of controlling magnetic states on the ultrafast timescale10-13 can be readily transferred to engineering the mechanical properties of nanodevices.

Mechanical Mode Imaging of a High-Q Hybrid hBN/Si3N4 Resonator

We image and characterize the mechanical modes of a 2D drum resonator made of hBN suspended over a high-stress Si₃N₄ membrane. Our measurements demonstrate hybridization between various modes of the hBN resonator and those of the Si₃N₄ membrane. The measured resonance frequencies and spatial profiles of the modes are consistent with finite-element simulations based on idealized geometry. Spectra of the thermal motion reveal that, depending on the degree of hybridization with modes of the heavier and higher-quality-factor Si₃N₄ membrane, the quality factors and the motional mass of the hBN drum modes can be shifted by orders of magnitude. This effect could be exploited to engineer hybrid drum/membrane modes that combine the low motional mass of 2D materials with the high quality factor of Si₃N₄ membranes for optomechanical or sensing applications.

2D-materials-integrated optoelectromechanics: recent progress and future perspectives

The discovery of two-dimensional (2D) materials has gained worldwide attention owing to their extraordinary optical, electrical, and mechanical properties. Due to their atomic layer thicknesses, the emerging 2D materials have great advantages of enhanced interaction strength, broad operating bandwidth, and ultralow power consumption for optoelectromechanical coupling. The van der Waals (vdW) epitaxy or multidimensional integration of 2D material family provides a promising platform for on-chip advanced nano-optoelectromechanical systems (NOEMS). Here, we provide a comprehensive review on the nanomechanical properties of 2D materials and the recent advances of 2D-materials-integrated nano-electromechanical systems and nano-optomechanical systems. By utilizing active nanophotonics and optoelectronics as the interface, 2D active NOEMS and their coupling effects are particularly highlighted at the 2D atomic scale. Finally, we share our viewpoints on the future perspectives and key challenges of scalable 2D-materials-integrated active NOEMS for on-chip miniaturized, lightweight, and multifunctional integration applications.

Electrically Tunable MXene Nanomechanical Resonators Vibrating at Very High Frequencies

As an emerging class of two-dimensional (2D) layered nanomaterial, MXene exhibits a number of intriguing properties, such as good electrical conductivity and high elastic modulus, and has witnessed continued growth in related device research. However, nanoscale MXene devices which leverage both the intrinsic electrical and mechanical properties of these 2D crystals have not been experimentally studied. Here we demonstrate nanoelectromechanical resonators based on 2D MXene crystals, where Ti₃C₂T_x drumheads with a wide range of thickness, from more than 50 layers all the way down to a monolayer, exhibit robust nanomechanical vibrations with fundamental-mode frequency f₀ up to >70 MHz in the very high frequency (VHF) band, a displacement noise density down to 52 fm/Hz^1/2, and a fundamental-mode frequency-quality factor product up to f₀ × Q ≈ 6.85 × 10⁹ Hz. By combining experimental results with theoretical calculations, we independently derive the Young's modulus of 2D Ti₃C₂T_x crystals to be 270-360 GPa, in excellent agreement with nanoindentation measurements, based on which we elucidate frequency scaling pathways toward microwave frequencies. We further demonstrate electrical tuning of resonance frequency in MXene resonators and frequency-shift-based MXene vacuum gauges with responsivity of 736%/Torr and detection range down to 10^-4 Torr. Our study can lead to the design and creation of nanoscale vibratory devices that exploit the intrinsic electrical and mechanical properties in 2D MXene crystals.

Sliding nanomechanical resonators

The motion of a vibrating object is determined by the way it is held. This simple observation has long inspired string instrument makers to create new sounds by devising elegant string clamping mechanisms, whereby the distance between the clamping points is modulated as the string vibrates. At the nanoscale, the simplest way to emulate this principle would be to controllably make nanoresonators slide across their clamping points, which would effectively modulate their vibrating length. Here, we report measurements of flexural vibrations in nanomechanical resonators that reveal such a sliding motion. Surprisingly, the resonant frequency of vibrations draws a loop as a tuning gate voltage is cycled. This behavior indicates that sliding is accompanied by a delayed frequency response of the resonators, making their dynamics richer than that of resonators with fixed clamping points. Our work elucidates the dynamics of nanomechanical resonators with unconventional boundary conditions, and offers opportunities for studying friction at the nanoscale from resonant frequency measurements.

The motion of a vibrating object is set by the way it is held. Here, the authors show a nanomechanical resonator reversibly slides on its supporting substrate as it vibrates and exploit this unconventional dynamics to quantify friction at the nanoscale.

Nanomechanical Resonators: Toward Atomic Scale

The quest for realizing and manipulating ever smaller man-made movable structures and dynamical machines has spurred tremendous endeavors, led to important discoveries, and inspired researchers to venture to previously unexplored grounds. Scientific feats and technological milestones of miniaturization of mechanical structures have been widely accomplished by advances in machining and sculpturing ever shrinking features out of bulk materials such as silicon. With the flourishing multidisciplinary field of low-dimensional nanomaterials, including one-dimensional (1D) nanowires/nanotubes and two-dimensional (2D) atomic layers such as graphene/phosphorene, growing interests and sustained effort have been devoted to creating mechanical devices toward the ultimate limit of miniaturization─genuinely down to the molecular or even atomic scale. These ultrasmall movable structures, particularly nanomechanical resonators that exploit the vibratory motion in these 1D and 2D nano-to-atomic-scale structures, offer exceptional device-level attributes, such as ultralow mass, ultrawide frequency tuning range, broad dynamic range, and ultralow power consumption, thus holding strong promises for both fundamental studies and engineering applications. In this Review, we offer a comprehensive overview and summary of this vibrant field, present the state-of-the-art devices and evaluate their specifications and performance, outline important achievements, and postulate future directions for studying these miniscule yet intriguing molecular-scale machines.

Monolayer MXene Nanoelectromechanical Piezo-Resonators with 0.2 Zeptogram Mass Resolution

2D materials-based nanoelectromechanical resonant systems with high sensitivity can precisely trace quantities of ultra-small mass molecules and therefore are broadly applied in biological analysis, chemical sensing, and physical detection. However, conventional optical and capacitive transconductance schemes struggle to measure high-order mode resonant effectively, which is the scientific key to further achieving higher accuracy and lower noise. In the present study, the different vibrations of monolayer Ti3 C2 Tx MXene piezo-resonators are investigated, and achieve a high-order f2,3 resonant mode with a ≈234.59 ± 0.05 MHz characteristic peak due to the special piezoelectrical structure of the Ti3 C2 Tx MXene layer. The effective measurements of signals have a low thermomechanical motion spectral density (9.66 ± 0.01  f m H z $\frac{{fm}}{{\sqrt {Hz} }}$ ) and an extensive dynamic range (118.49 ± 0.42 dB) with sub-zeptograms resolution (0.22 ± 0.01 zg) at 300 K temperature and 1 atm. Furthermore, the functional groups of the Ti3 C2 Tx MXene with unique adsorption properties enable a high working range ratio of ≈3100 and excellent repeatability. This Ti3 C2 Tx MXene device demonstrates encouraging performance advancements over other nano-resonators and will lead the related engineering applications including high-sensitivity mass detectors.

Raman Spectroscopic Probe for Nonlinear MoS2 Nanoelectromechanical Resonators

Resonant nanoelectromechanical systems (NEMS) enabled by two-dimensional (2D) semiconductors have been actively explored and engineered for making ultrascaled transducers toward applications in ultralow-power signal processing, communication, and sensing. Although the transduction of miniscule resonant motions has been achieved by low-noise optical or electronic techniques, direct probing of strain in vibrating 2D semiconductor membranes and the interplay between the spectroscopic and mechanical properties are still largely unexplored. Here, we experimentally demonstrate dynamical phonon softening in atomically thin molybdenum disulfide (MoS₂) NEMS resonators by directly coupling Raman spectroscopy with optical interferometry resonance motion detection. In single-layer, bilayer, and trilayer (1L to 3L) MoS₂ circular membrane NEMS resonators, we show that high-amplitude nonlinear resonances can enhance the Raman signal amplitude, as well as introduce Raman modes softening up to 0.8 cm^-1. These results shall pave the way for engineering the coupling and control between collective mechanical vibrations and Raman modes of the constituent crystals in 2D transducers.

Kirigami Engineering of Suspended Graphene Transducers

The low mass density and high mechanical strength of graphene make it an attractive candidate for suspended-membrane energy transducers. Typically, the membrane size dictates the operational frequency and bandwidth. However, in many cases it would be desirable to both lower the resonance frequency and increase the bandwidth, while maintaining overall membrane size. We employ focused ion beam milling or laser ablation to create kirigami-like modification of suspended pure-graphene membranes ranging in size from microns to millimeters. Kirigami engineering successfully reduces the resonant frequency, increases the displacement amplitude, and broadens the effective bandwidth of the transducer. Our results present a promising route to miniaturized wide-band energy transducers with enhanced operational parameter range and efficiency.

Simultaneous ground-state cooling of identical mechanical oscillators by Lyapunov control

The simultaneous cooling of multiple mechanical oscillators in the cavity optomechanical system has aroused people's attention and may be applicable in the quantum information process. In this paper, a scheme to realize the simultaneous ground-state cooling of two identical mechanical oscillators is proposed, where the frequency of one of the oscillators is designed according to Lyapunov control. By this method, the dark mode can effectively couple with the bright mode so that the two identical oscillators can be simultaneously cooled to their ground state. Extending this scheme into multiple identical mechanical oscillators, we show that simultaneous cooling can also be achieved.

Highly Efficient Cellular Acoustic Absorber of Graphene Ultrathin Drums

Atomically thin 2D graphene sheets exhibit unparalleled in-plane stiffness and large out-of-plane elasticity, thereby providing strong mechanical resonance for nanomechanical devices. The exceptional resonance behavior of ultrathin graphene, which promises the fabrication of superior acoustic absorption materials, however, remains unfulfilled for the lack of applicable form and assembly methods. Here, a highly efficient acoustic absorber is presented, wherein cellular networks of ultrathin graphene membranes are constructed into polymer foams. The ultrathin graphene drums exhibit strong resonances and efficiently dissipate sound waves in a broad frequency range. A record specific noise reduction coefficient (51.3 at 30 mm) is achieved in the graphene-based acoustic absorber, fully realizing the superior resonance properties of graphene sheets. The scalable method facilely transforms commercial polymer foams to superior acoustic absorbers with a ≈320% enhancement in average absorption coefficient across wide frequencies from 200 to 6000 Hz. The graphene acoustic absorber offers a convenient method to exploit the extraordinary resonance properties of 2D sheets, opening extensive new applications in noise protection, building design, instruments and acoustic devices.

Real-time nanomechanical property modulation as a framework for tunable NEMS

Phase-change materials (PCMs) can switch between amorphous and crystalline states permanently yet reversibly. However, the change in their mechanical properties has largely gone unexploited. The most practical configuration using suspended thin-films suffer from filamentation and melt-quenching. Here, we overcome these limitations using nanowires as active nanoelectromechanical systems (NEMS). We achieve active modulation of the Young’s modulus in GeTe nanowires by exploiting a unique dislocation-based route for amorphization. These nanowire NEMS enable power-free tuning of the resonance frequency over a range of 30%. Furthermore, their high quality factors (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Q$$\end{document}Q > 10⁴) are retained after phase transformation. We utilize their intrinsic piezoresistivity with unprecedented gauge factors (up to 1100) to facilitate monolithic integration. Our NEMS demonstrate real-time frequency tuning in a frequency-hopping spread spectrum radio prototype. This work not only opens up an entirely new area of phase-change NEMS but also provides a novel framework for utilizing functional nanowires in active mechanical systems.

Direct modulation of Young‟s Modulus to affect mechanical resonances in real-time has not been achieved before. Here, the authors leverage the dislocation migration phenomenon in GeTe nanowires to develop nanoelectromechanical systems with powerfree tuning of mechanical resonances within a range of 30%, high and stable quality and gauge factors.

Strain-Modulated Dissipation in Two-Dimensional Molybdenum Disulfide Nanoelectromechanical Resonators

Resonant nanoelectromechanical systems (NEMS) based on two-dimensional (2D) materials such as molybdenum disulfide (MoS₂) are interesting for highly sensitive mass, force, photon, or inertial transducers, as well as for fundamental research approaching the quantum limit, by leveraging the mechanical degree of freedom in these atomically thin materials. For these mechanical resonators, the quality factor (Q) is essential, yet the mechanism and tuning methods for energy dissipation in 2D NEMS resonators have not been fully explored. Here, we demonstrate that by tuning static strain and vibration-induced strain in suspended MoS₂ using gate voltages, we can effectively tune the Q in 2D MoS₂ NEMS resonators. We further show that for doubly clamped resonators, the Q increases with larger DC gate voltage, while fully clamped drumhead resonators show the opposite trend. Using DC gate voltages, we can tune the Q by ΔQ/Q = 448% for fully clamped resonators, and by ΔQ/Q = 369% for doubly clamped resonators. We develop the strain-modulated dissipation model for these 2D NEMS resonators, which is verified against our measurement data for 8 fully clamped resonators and 7 doubly clamped resonators. We find that static tensile strain decreases dissipation while vibration-induced strain increases dissipation, and the actual dependence of Q on DC gate voltage depends on the competition between these two effects, which is related to the device boundary condition. Such strain dependence of Q is useful for optimizing the resonance linewidth in 2D NEMS resonators toward low-power, ultrasensitive, and frequency-selective devices for sensing and signal processing.

Fabry-Perot interferometric calibration of van der Waals material-based nanomechanical resonators

One of the challenges in integrating nanomechanical resonators made from van der Waals materials in optoelectromechanical technologies is characterizing their dynamic properties from vibrational displacement. Multiple calibration schemes using optical interferometry have tackled this challenge. However, these techniques are limited only to optically thin resonators with an optimal vacuum gap height and substrate for interferometric detection. Here, we address this limitation by implementing a modeling-based approach via multilayer thin-film interference for in situ, non-invasive determination of the resonator thickness, gap height, and motional amplitude. This method is demonstrated on niobium diselenide drumheads that are electromotively driven in their linear regime of motion. The laser scanning confocal configuration enables a resolution of hundreds of picometers in motional amplitude for circular and elliptical devices. The measured thickness and spacer height, determined to be in the order of tens and hundreds of nanometers, respectively, are in excellent agreement with profilometric measurements. Moreover, the transduction factor estimated from our method agrees with the result of other studies that resolved Brownian motion. This characterization method, which applies to both flexural and acoustic wave nanomechanical resonators, is robust because of its scalability to thickness and gap height, and any form of reflecting substrate.

Tunable Strong Coupling of Mechanical Resonance between Spatially Separated FePS3 Nanodrums

Coupled nanomechanical resonators made of two-dimensional materials are promising for processing information with mechanical modes. However, the challenge for these systems is to control the coupling. Here, we demonstrate strong coupling of motion between two suspended membranes of the magnetic 2D material FePS₃. We describe a tunable electromechanical mechanism for control over both the resonance frequency and the coupling strength using a gate voltage electrode under each membrane. We show that the coupling can be utilized for transferring data between drums by amplitude modulation. Finally, we also study the temperature dependence of the coupling and how it is affected by the antiferromagnetic phase transition characteristic of this material. The presented electrical coupling of resonant magnetic 2D membranes holds the promise of transferring mechanical energy over a distance at low electrical power, thus enabling novel data readout and information processing technologies.

Thermal hysteresis controlled reconfigurable MoS2 nanomechanical resonators

Two-dimensional (2D) structures from layered materials have enabled a number of novel devices including resonant nanoelectromechanical systems (NEMS). 2D NEMS resonators are highly responsive to strain, allowing their resonance frequencies to be efficiently tuned over broad ranges, which is a feature difficult to attain in conventional micromachined resonators. In electrically configured and tuned devices, high external voltages are typically required to set and maintain different frequencies, limiting their applications. Here we experimentally demonstrate molybdenum disulfide (MoS₂) nanomechanical resonators that can be reconfigured between different frequency bands with zero maintaining voltage in a non-volatile fashion. By leveraging the thermal hysteresis in these 2D resonators, we use heating and cooling pulses to reconfigure the device frequency, with no external voltage required to maintain each frequency. We further show that the frequency spacing between the bands can be tuned by the thermal pulse strength, offering full control over the programmable operation. Such reconfigurable MoS₂ resonators may provide an alternative pathway toward small-form-factor and low-power tunable devices in future reconfigurable radio-frequency circuits with multi-band capability.

Ferroelectric 2D ice under graphene confinement

We here report on the direct observation of ferroelectric properties of water ice in its 2D phase. Upon nanoelectromechanical confinement between two graphene layers, water forms a 2D ice phase at room temperature that exhibits a strong and permanent dipole which depends on the previously applied field, representing clear evidence for ferroelectric ordering. Characterization of this permanent polarization with respect to varying water partial pressure and temperature reveals the importance of forming a monolayer of 2D ice for ferroelectric ordering which agrees with ab-initio and molecular dynamics simulations conducted. The observed robust ferroelectric properties of 2D ice enable novel nanoelectromechanical devices that exhibit memristive properties. A unique bipolar mechanical switching behavior is observed where previous charging history controls the transition voltage between low-resistance and high-resistance state. This advance enables the realization of rugged, non-volatile, mechanical memory exhibiting switching ratios of 10⁶, 4 bit storage capabilities and no degradation after 10,000 switching cycles.

Ferroelectric ordering of water has been at the heart of intense debates due to its importance in enhancing our understanding of the condensed matter. Here, the authors observe ferroelectric properties of water ice in a two dimensional phase under confinement between two graphene layers.

Graphene-Based Nanoelectromechanical Periodic Array with Tunable Frequency

Phononic crystals (PnCs) have attracted much attention due to their great potential for dissipation engineering and propagation manipulation of phonons. Notably, the excellent electrical and mechanical properties of graphene make it a promising material for nanoelectromechanical resonators. Transferring a graphene flake to a prepatterned periodic mechanical structure enables the realization of a PnC with on-chip scale. Here, we demonstrate a nanoelectromechanical periodic array by anchoring a graphene membrane to a 9 × 9 array of standing nanopillars. The device exhibits a quasi-continuous frequency spectrum with resonance modes distributed from ∼120 MHz to ∼980 MHz. Moreover, the resonant frequencies of these modes can be electrically tuned by varying the voltage applied to the gate electrode sitting underneath. Simulations suggest that the observed band-like spectrum provides an experimental evidence for PnC formation. Our architecture has large fabrication flexibility, offering a promising platform for investigations on PnCs with electrical accessibility and tunability.

Dissipation from Interlayer Friction in Graphene Nanoelectromechanical Resonators

A unique feature of two-dimensional (2D) materials is the ultralow friction at their van der Waals interfaces. A key question in a new generation of 2D heterostructure-based nanoelectromechanical systems (NEMS) is how the low friction interfaces will affect the dynamic performance. Here, we apply the exquisite sensitivity of graphene nanoelectromechanical drumhead resonators to compare the dissipation from monolayer, Bernal-stacked bilayer, and twisted bilayer graphene membranes. We find a significant difference in the average quality factors of three resonator types: 53 for monolayer, 40 for twisted and 31 for Bernal-stacked membranes. We model this difference as a combination of change in stiffness and additional dissipation from interlayer friction during motion. We find even the lowest frictions measured on sliding 2D interfaces are sufficient to alter dissipation in 2D NEMS. This model provides a generalized approach to quantify dissipation in NEMS based on 2D heterostructures which incorporate interlayer slip and friction.

Optical-Thermally Excited Graphene Resonant Mass Detection: A Molecular Dynamics Analysis

In consideration of the presented optical-thermally excited resonant mass detection scheme, molecular dynamics calculations are performed to investigate the thermal actuation and resonant mass sensing mechanism. The simulation results indicate that an extremely high temperature exists in a 6% central area of the graphene sheet exposed to the exciting laser. Therefore, constraining the laser driving power and enlarging the laser spot radius are essential to weaken the overheating in the middle of the graphene sheet, thus avoiding being burned through. Moreover, molecular dynamics calculations demonstrate a mass sensitivity of 214 kHz/zg for the graphene resonator with a pre-stress of 1 GPa. However, the adsorbed mass would degrade the resonant quality factor from 236 to 193. In comparison, the sensitivity and quality factor could rise by 1.3 and 4 times, respectively, for the graphene sheet with a pre-stress of 5 GPa, thus revealing the availability of enlarging pre-stress for better mass sensing performance.

Ultrawide Frequency Tuning of Atomic Layer van der Waals Heterostructure Electromechanical Resonators

We report on the experimental demonstration of atomically thin molybdenum disulfide (MoS₂)-graphene van der Waals (vdW) heterostructure nanoelectromechanical resonators with ultrawide frequency tuning. With direct electrostatic gate tuning, these vdW resonators exhibit exceptional tunability, in general, Δf/f₀ > 200%, for continuously tuning the same device and the same mode (e.g., from ∼23 to ∼107 MHz), up to Δf/f₀ ≈ 370%, the largest fractional tuning range in such resonators to date. This remarkable electromechanical resonance tuning is investigated by two different analytical models and finite element simulations. Furthermore, we carefully perform clear control experiments and simulations to elucidate the difference in frequency tuning between the heterostructure and single-material resonators. At a given initial strain level, the tuning range depends on the two-dimensional (2D) Young's moduli of the constitutive crystals; devices built on materials with lower 2D moduli show wider tuning ranges. This study exemplifies that vdW heterostructure resonators can retain unconventionally broad, continuous tuning, which is promising for voltage-controlled, tunable nanosystems.

Detection of SARS-CoV-2 Using Antibody-Antigen Interactions with Graphene-Based Nanomechanical Resonator Sensors

Coronavirus disease 2019 (COVID-19) is a newly emerging human infectious disease caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Early diagnosis is essential to reducing the transmission rate and mortality of COVID-19. PCR-based tests are the gold standard for the confirmation of COVID-19, but immunological tests for SARS-CoV-2 detection are widely available and play an increasingly important role in the diagnosis of COVID-19. Nanomechanical sensors are biosensors that work based on a change in the mechanical response of the system when a foreign object is added. In this paper, a graphene-based nanoresonator sensor for SARS-CoV-2 detection was introduced and analyzed by using the finite element method (FEM). The sensor was simulated by coating a single-layer graphene sheet (SLGS) with a specific antibody against SARS-CoV-2 Spike S1 antigen. In the following, the SARS-CoV-2 viruses were randomly distributed on the SLGSs, and essential design parameters of the nanoresonator, including frequency shift and relative frequency shift, were evaluated. The effect of the SLGS size, aspect ratio and boundary conditions, antibody concentration, and the number of viruses variation on the frequency shift and relative frequency shift were investigated. The results revealed that, by proper selection of the nanoresonator design variables, a good sensitivity index is achievable for identifying the SARS-CoV-2 virus even when the number of the viruses are less than 10 per test. Eventually, according to the simulation results, by using SLGS geometry determination, an analytical relationship is presented to predict the limit of detection (LOD) of the sensor with the required sensitivity index. The results can be applied in designing and fabricating specific graphene-based nanoresonator sensors for SARS-CoV-2.

The Recent Progress of MEMS/NEMS Resonators

MEMS/NEMS resonators are widely studied in biological detection, physical sensing, and quantum coupling. This paper reviews the latest research progress of MEMS/NEMS resonators with different structures. The resonance performance, new test method, and manufacturing process of single or double-clamped resonators, and their applications in mass sensing, micromechanical thermal analysis, quantum detection, and oscillators are introduced in detail. The material properties, resonance mode, and application in different fields such as gyroscope of the hemispherical structure, microdisk structure, drum resonator are reviewed. Furthermore, the working principles and sensing methods of the surface acoustic wave and bulk acoustic wave resonators and their new applications such as humidity sensing and fast spin control are discussed. The structure and resonance performance of tuning forks are summarized. This article aims to classify resonators according to different structures and summarize the working principles, resonance performance, and applications.

Tunable parametric amplification of a graphene nanomechanical resonator in the nonlinear regime

Parametric amplification is widely used in nanoelectro-mechanical systems to enhance the transduced mechanical signals. Although parametric amplification has been studied in different mechanical resonator systems, the nonlinear dynamics involved receives less attention. Taking advantage of the excellent electrical and mechanical properties of graphene, we demonstrate electrical tunable parametric amplification using a doubly clamped graphene nanomechanical resonator. By applying external microwave pumping with twice the resonant frequency, we investigate parametric amplification in the nonlinear regime. We experimentally show that the extracted coefficient of the nonlinear Duffing force α and the nonlinear damping coefficient η vary as a function of external pumping power, indicating the influence of higher-order nonlinearity beyond the Duffing (∼x ³) and van der Pol (∼[Formula: see text]) types in our device. Even when the higher-order nonlinearity is involved, parametric amplification still can be achieved in the nonlinear regime. The parametric gain increases and shows a tendency of saturation with increasing external pumping power. Further, the parametric gain can be electrically tuned by the gate voltage with a maximum gain of 10.2 dB achieved at the gate voltage of 19 V. Our results will benefit studies on nonlinear dynamics, especially nonlinear damping in graphene nanomechanical resonators that has been debated in the community over past decade.

Tunable Exciton-Optomechanical Coupling in Suspended Monolayer MoSe2

The strong excitonic effect in monolayer transition metal dichalcogenide (TMD) semiconductors has enabled many fascinating light-matter interaction phenomena. Examples include strongly coupled exciton-polaritons and nearly perfect atomic monolayer mirrors. The strong light-matter interaction also opens the door for dynamical control of mechanical motion through the exciton resonance of monolayer TMDs. Here, we report the observation of exciton-optomechanical coupling in a suspended monolayer MoSe₂ mechanical resonator. By moderate optical pumping near the MoSe₂ exciton resonance, we have observed optical damping and antidamping of mechanical vibrations as well as the optical spring effect. The exciton-optomechanical coupling strength is also gate-tunable. Our observations can be understood in a model based on photothermal backaction and gate-induced mirror symmetry breaking in the device structure. The observation of gate-tunable exciton-optomechanical coupling in a monolayer semiconductor may find applications in nanoelectromechanical systems (NEMS) and in exciton-optomechanics.

Tunable Graphene Phononic Crystal

In the field of phononics, periodic patterning controls vibrations and thereby the flow of heat and sound in matter. Bandgaps arising in such phononic crystals (PnCs) realize low-dissipation vibrational modes and enable applications toward mechanical qubits, efficient waveguides, and state-of-the-art sensing. Here, we combine phononics and two-dimensional materials and explore tuning of PnCs via applied mechanical pressure. To this end, we fabricate the thinnest possible PnC from monolayer graphene and simulate its vibrational properties. We find a bandgap in the megahertz regime within which we localize a defect mode with a small effective mass of 0.72 ag = 0.002 m_physical. We exploit graphene's flexibility and simulate mechanical tuning of a finite size PnC. Under electrostatic pressure up to 30 kPa, we observe an upshift in frequency of the entire phononic system by ∼350%. At the same time, the defect mode stays within the bandgap and remains localized, suggesting a high-quality, dynamically tunable mechanical system.

Dissipative bosonic squeezing via frequency modulation and its application in optomechanics

The dissipative squeezing mechanism is an effective method to generate the strong squeezing, which is important in the precision metrology. Here, we propose a practical method to achieve arbitrary bosonic squeezing via introducing frequency modulation into the coupled harmonic resonator model. We analyze the effect of frequency modulation and give the analytical and numerical squeezing results, respectively. To measure the accurate dynamic squeezing in our proposal, we give a more general defination of the relative squeezing degree. Finally, the proposed method is extended to generate the strong mechanical squeezing (>3 dB) in a practical optomechanical system consisting of a graphene mechanical oscillator coupled to a superconducting microwave cavity. The result indicates that the strong mechanical squeezing can be effectively achieved even when the mechanical oscillator is not initially in its ground state. The proposed method expands the study on nonclassical state and does not need the bichromatic microwave driving technology.

Approaching the Strain-Free Limit in Ultrathin Nanomechanical Resonators

Ultrathin mechanical structures are ideal building platforms to pursue the ultimate limit of nanomechanical resonators for applications in sensing, signal processing, and quantum physics. Unfortunately, as the thickness of the vibrating structures is reduced, the built-in strain of the structural materials plays an increased role in determining the mechanical performance of the devices. As a consequence, it is very challenging to fabricate resonators working in the modulus-dominant regime, where their dynamic behavior is exclusively determined by the device geometry. In this Letter, we report ultrathin doubly clamped nanomechanical resonators with aspect ratios as large as L/t ∼5000 and working in the modulus-dominant regime. We observed room temperature thermomechanically induced motion of multiple vibration modes with resonant frequencies closely matching the predicted values of Euler-Bernoulli beam theory under an axial strain of 6.3 × 10^-8. The low strain of the devices enables a record frequency tuning ratio of more than 50 times. These results illustrate a new strategy for the quantitative design of nanomechanical resonators with unprecedented performance.

Nanoelectromechanical Sensors Based on Suspended 2D Materials

The unique properties and atomic thickness of two-dimensional (2D) materials enable smaller and better nanoelectromechanical sensors with novel functionalities. During the last decade, many studies have successfully shown the feasibility of using suspended membranes of 2D materials in pressure sensors, microphones, accelerometers, and mass and gas sensors. In this review, we explain the different sensing concepts and give an overview of the relevant material properties, fabrication routes, and device operation principles. Finally, we discuss sensor readout and integration methods and provide comparisons against the state of the art to show both the challenges and promises of 2D material-based nanoelectromechanical sensing.

Transformation and Evaporation of Surface Adsorbents on a Graphene "Hot Plate"

Dynamic surface modification of suspended graphene at high temperatures was directly observed with in situ scanning transmission electron microscopy (STEM) measurements. The suspended graphene devices were prepared on a SiN membrane substrate with a hole so that STEM observations could be conducted during Joule heating. Current-voltage characteristics of suspended graphene devices inside the STEM chamber were measured while monitoring and controlling the temperature of graphene by estimating the electrical power of the devices. During the in situ STEM observation at high temperatures, residual hydrocarbon adsorbents that had remained on graphene effectively evaporated creating large, atomically clean graphene areas. At other places, dynamic changes in the shape, position, and orientation of adsorbents could be directly observed. The temperature of the suspended graphene sample was estimated to reach up to 2000 K during the experiment, making graphene an efficient high-temperature micrometer-sized electron-transparent hot plate for future experiments in microscopes.

Magnetic and electronic phase transitions probed by nanomechanical resonators

The reduced dimensionality of two-dimensional (2D) materials results in characteristic types of magnetically and electronically ordered phases. However, only few methods are available to study this order, in particular in ultrathin insulating antiferromagnets that couple weakly to magnetic and electronic probes. Here, we demonstrate that phase transitions in thin membranes of 2D antiferromagnetic FePS₃, MnPS₃ and NiPS₃ can be probed mechanically via the temperature-dependent resonance frequency and quality factor. The observed relation between mechanical motion and antiferromagnetic order is shown to be mediated by the specific heat and reveals a strong dependence of the Néel temperature of FePS₃ on electrostatically induced strain. The methodology is not restricted to magnetic order, as we demonstrate by probing an electronic charge-density-wave phase in 2H-TaS₂. It thus offers the potential to characterize phase transitions in a wide variety of materials, including those that are antiferromagnetic, insulating or so thin that conventional bulk characterization methods become unsuitable.

Fatigue of graphene

Materials can suffer mechanical fatigue when subjected to cyclic loading at stress levels much lower than the ultimate tensile strength, and understanding this behaviour is critical to evaluating long-term dynamic reliability. The fatigue life and damage mechanisms of two-dimensional (2D) materials, of interest for mechanical and electronic applications, are currently unknown. Here, we present a fatigue study of freestanding 2D materials, specifically graphene and graphene oxide (GO). Using atomic force microscopy, monolayer and few-layer graphene were found to exhibit a fatigue life of more than 10⁹ cycles at a mean stress of 71 GPa and a stress range of 5.6 GPa, higher than any material reported so far. Fatigue failure in monolayer graphene is global and catastrophic without progressive damage, while molecular dynamics simulations reveal this is preceded by stress-mediated bond reconfigurations near defective sites. Conversely, functional groups in GO impart a local and progressive fatigue damage mechanism. This study not only provides fundamental insights into the fatigue enhancement behaviour of graphene-embedded nanocomposites, but also serves as a starting point for the dynamic reliability evaluation of other 2D materials.

Conductance of Buckled N = 5 Armchair Graphene Nanoribbons

Electromechanical coupling in graphene nanoribbons has been the focus of much basic research. Although ab initio methods have been used to compute the current-voltage characteristics of deformed nanoribbons, analytical models that embody fundamental quantum electron transmission concepts are needed to support the conceptual design of new nanoelectromechanical devices. Numerical analysis of the conduction properties of buckled armchair graphene nanoribbons indicates that, consistent with experiment, the bending effects on current flow in rippled nanoribbons are determined by an integral measure of the total rotation along the conductor, which accounts for scattering effects accumulated along the entire transport path. The modeling results provide the first general description of both length and bending effects on current flow in semiconducting nanowires.

Stochastic Stress Jumps Due to Soliton Dynamics in Two-Dimensional van der Waals Interfaces

The creation and movement of dislocations determine the nonlinear mechanics of materials. At the nanoscale, the number of dislocations in structures become countable, and even single defects impact material properties. While the impact of solitons on electronic properties is well studied, the impact of solitons on mechanics is less understood. In this study, we construct nanoelectromechanical drumhead resonators from Bernal stacked bilayer graphene and observe stochastic jumps in frequency. Similar frequency jumps occur in few-layer but not twisted bilayer or monolayer graphene. Using atomistic simulations, we show that the measured shifts are a result of changes in stress due to the creation and annihilation of individual solitons. We develop a simple model relating the magnitude of the stress induced by soliton dynamics across length scales, ranging from <0.01 N/m for the measured 5 μm diameter to ∼1.2 N/m for the 38.7 nm simulations. These results demonstrate the sensitivity of 2D resonators are sufficient to probe the nonlinear mechanics of single dislocations in an atomic membrane and provide a model to understand the interfacial mechanics of different kinds of van der Waals structures under stress, which is important to many emerging applications such as engineering quantum states through electromechanical manipulation and mechanical devices like highly tunable nanoelectromechanical systems, stretchable electronics, and origami nanomachines.

Dry transfer method for suspended graphene on lift-off-resist: simple ballistic devices with Fabry-Pérot interference

We demonstrate a fabrication scheme for clean suspended structures using chemical-vapor-deposition-grown graphene and a dry transfer method on lift-off-resist-coated substrates to facilitate suspended graphene nanoelectronic devices for technological applications. It encompasses the demands for scalable fabrication as well as for ultra-fast response due to weak coupling to environment. The fabricated devices exhibited initially a weak field-effect response with substantial positive (p) doping which transformed into weak negative (n) doping upon current annealing at the temperature of 4 K. With increased annealing current, n-doping gradually decreased while the Dirac peak position approached zero in gate voltage. An ultra-low residual charge density of 9 × 10⁸ cm^-2 and a mobility of 1.9 × 10⁵ cm² V^-1 s^-1 were observed. Our samples display clear Fabry-Pérot (FP) conductance oscillation which indicates ballistic electron transport. The spacings of the FP oscillations are found to depend on the charge density in a manner that agrees with theoretical modeling based on Klein tunneling of Dirac particles. The ultra-low residual charge, the FP oscillations with density dependent period, and the high mobility prove the excellent quality of our suspended graphene devices. Owing to its simplicity, scalability and robustness, this fabrication scheme enhances possibilities for production of suspended, high-quality, two-dimensional-material structures for novel electronic applications.

Experimental realization of on-chip topological nanoelectromechanical metamaterials

Guiding waves through a stable physical channel is essential for reliable information transport. However, energy transport in high-frequency mechanical systems, such as in signal-processing applications¹, is particularly sensitive to defects and sharp turns because of back-scattering and losses². Topological phenomena in condensed matter systems have shown immunity to defects and unidirectional energy propagation³. Topological mechanical metamaterials translate these properties into classical systems for efficient phononic energy transport. Acoustic and mechanical topological metamaterials have so far been realized only in large-scale systems, such as arrays of pendulums⁴, gyroscopic lattices^5,6, structured plates^7,8 and arrays of rods, cans and other structures acting as acoustic scatterers^9-12. To fulfil their potential in device applications, mechanical topological systems need to be scaled to the on-chip level for high-frequency transport^13-15. Here we report the experimental realization of topological nanoelectromechanical metamaterials, consisting of two-dimensional arrays of free-standing silicon nitride nanomembranes that operate at high frequencies (10-20 megahertz). We experimentally demonstrate the presence of edge states, and characterize their localization and Dirac-cone-like frequency dispersion. Our topological waveguides are also robust to waveguide distortions and pseudospin-dependent transport. The on-chip integrated acoustic components realized here could be used in unidirectional waveguides and compact delay lines for high-frequency signal-processing applications.

Nano-electromechanical Drumhead Resonators from Two-Dimensional Material Bimorphs

Atomic membranes of monolayer 2D materials represent the ultimate limit in the size of nano-electromechanical systems. However, new properties and new functionalities emerge by looking at the interface between layers in heterostructures of 2D materials. Here, we demonstrate the integration of 2D heterostructures as tunable nano-electromechanical systems, exploring the competition between the mechanics of the ultrathin membrane and the incommensurate van der Waals interface. We fabricate electrically contacted 5 or 6 μm circular drumheads of suspended heterostructure membranes of monolayer graphene on monolayer molybdenum disulfide (MoS₂), which we call a 2D bimorph. We characterize the mechanical resonance through electrostatic actuation and laser interferometry detection. The 2D bimorphs have resonance frequencies of 5-20 MHz and quality factors of 50-700, comparable to resonators from monolayer or few-layer 2D materials. The frequencies and eigenmode shapes of the higher harmonics display split degenerate modes, showing that the 2D bimorphs behave as membranes with asymmetric tension. The devices display dynamic ranges of 44 dB, with an additional nonlinearity in the dissipation at small drive. Under electrostatic frequency tuning, devices display a small tuning of ∼20% compared with graphene resonators, which have >100%. In addition, the tuning shows a kink that deviates from the tensioned membrane model for atomic membranes and corresponds with a changing in stress of 14 mN/m. A model that accounts for this tuning behavior is the onset of interlayer slip in the heterostructure, allowing the tension in the membrane to relax. Using density functional theory simulations, we find that the change in stress at the kink is much larger than the predicted energy barrier for interlayer slip of 0.102 mN/m in an incommensurate 2D heterostructure but smaller than the energy barrier for an aligned graphene bilayer of 35 mN/m, suggesting a local pinning effect at ripples or folds in the heterostructure. Finally, we observe an asymmetry in tuning of the full width at half-maximum that does not exist in monolayer resonators. These findings demonstrate a new class of nano-electromechanical systems from 2D heterostructures and unravel the complex interaction of membrane morphology versus interlayer adhesion and slip on the mechanics of incommensurate van der Waals interfaces.

Electrical tuning of elastic wave propagation in nanomechanical lattices at MHz frequencies

Nanoelectromechanical systems (NEMS) that operate in the megahertz (MHz) regime allow energy transducibility between different physical domains. For example, they convert optical or electrical signals into mechanical motions and vice versa¹. This coupling of different physical quantities leads to frequency-tunable NEMS resonators via electromechanical non-linearities^2-4. NEMS platforms with single- or low-degrees of freedom have been employed to demonstrate quantum-like effects, such as mode cooling⁵, mechanically induced transparency⁵, Rabi oscillation^6,7, two-mode squeezing⁸ and phonon lasing⁹. Periodic arrays of NEMS resonators with architected unit cells enable fundamental studies of lattice-based solid-state phenomena, such as bandgaps^10,11, energy transport^10-12, non-linear dynamics and localization^13,14, and topological properties¹⁵, directly transferrable to on-chip devices. Here we describe one-dimensional, non-linear, nanoelectromechanical lattices (NEML) with active control of the frequency band dispersion in the radio-frequency domain (10-30 MHz). The design of our systems is inspired by NEMS-based phonon waveguides^10,11 and includes the voltage-induced frequency tuning of the individual resonators^2-4. Our NEMLs consist of a periodic arrangement of mechanically coupled, free-standing nanomembranes with circular clamped boundaries. This design forms a flexural phononic crystal with a well-defined bandgap, 1.8 MHz wide. The application of a d.c. gate voltage creates voltage-dependent on-site potentials, which can significantly shift the frequency bands of the device. Additionally, a dynamic modulation of the voltage triggers non-linear effects, which induce the formation of a phononic bandgap in the acoustic branch, analogous to Peierls transition in condensed matter¹⁶. The gating approach employed here makes the devices more compact than recently proposed systems, whose tunability mostly relies on materials' compliance^17,18 and mechanical non-linearities^19-22.