MoS2 nanoresonators: intrinsically better than graphene?

Nonlinear coupling of closely spaced modes in atomically thin MoS2 nanoelectromechanical resonators

Nanoelectromechanical systems (NEMS) incorporating atomic or molecular layer van der Waals materials can support multimode resonances and exotic nonlinear dynamics. Here we investigate nonlinear coupling of closely spaced modes in a bilayer (2L) molybdenum disulfide (MoS2) nanoelectromechanical resonator. We model the response from a drumhead resonator using equations of two resonant modes with a dispersive coupling term to describe the vibration induced frequency shifts that result from the induced change in tension. We employ method of averaging to solve the equations of coupled modes and extract an expression for the nonlinear coupling coefficient (λ) in closed form. Undriven thermomechanical noise spectral measurements are used to calibrate the vibration amplitude of mode 2 (a2) in the displacement domain. We drive mode 2 near its natural frequency and measure the shifted resonance frequency of mode 1 (f1s) resulting from the dispersive coupling. Our model yields λ = 0.027 ± 0.005 pm-2 · μs-2 from thermomechanical noise measurement of mode 1. Our model also captures an anomalous frequency shift of the undriven mode 1 due to nonlinear coupling to the driven mode 2 mediated by large dynamic tension. This study provides a direct means to quantifying λ by measuring the thermomechanical noise in NEMS and will be valuable for understanding nonlinear mode coupling in emerging resonant systems.

Enhanced Pressure Response of Edge-Deposited Graphene Nanomechanical Resonators

Nanomechanical resonators made of suspended graphene exhibit high sensitivity to pressure changes. Nevertheless, the graphene resonator pressure performance is affected owing to the gas permeation problem between the graphene film and the substrate. Therefore, we prepared edge-deposited graphene resonators by focused ion beam (FIB) deposition of SiO2, and their gas leakage velocities and pressure-sensing ability were demonstrated. In this paper, we characterize the pressure-sensing response and gas leakage velocities of graphene membranes using an all-optical actuation system. The gas leakage velocities of graphene resonators with diameters of 10, 20, and 40 μm are reduced by 5.0 × 106, 2.0 × 107, and 8.1 × 107 atoms/s, respectively, which demonstrates that the edge deposition structure can reduce the gas leakage of the resonator. Furthermore, the pressure-sensing performance of three graphene resonators with different diameters was evaluated, and their average pressure sensitivities were calculated to be 3.4, 2.4, and 1.9 kHz/kPa, with the largest full-range hysteresis errors of 0.6, 0.7, and 1.0%, respectively. The temperature stabilities of the three sizes of resonators in the temperature range of 300-400 K are 0.016, 0.015, and 0.016%/K, and the maximum resonance frequency drift over 1 h is 0.0058, 0.0048, and 0.0112%, respectively. This work has great significance for the improvement of gas leakage velocity characterization of graphene membrane and graphene resonant pressure sensor performance optimization.

Probing Thermal Transport on a Suspended Ti3C2Tx MXene Film via a Photothermally Actuated Resonator

Two-dimensional (2D) Ti3C2Tx MXene materials show great potential in electrochemical and flexible sensors due to their high electrical conductivity, good chemical stability, and special delaminated structure. However, their thermal properties were rarely studied, which remarkably affect the stability and safety of various devices. Here, we fabricated a suspended MXene drum resonator photothermally driven by a sinusoidally modulated laser, measured the thermal time constant by demodulating the thermomechanical motion, and then calculated the thermal conductivity and thermal diffusivity of the MXene film. Experiments show the thermal conductivity of the film increases from 3.10 to 3.58 W/m·K while the thermal diffusivity from 1.06 × 10-6 to 1.22 × 10-6 m2/s when temperature increases from 300 to 360 K. We also confirm the film thermal conductivity is mainly contributed by phonon transport rather than electron transport. Furthermore, the relationship between the mechanical and thermal properties of the MXene films was disclosed. The thermal conductivity decreases when film strain increases, caused by enhanced phonon scattering and softening of high-frequency phonons. The measurements provide a noninvasive method to analyze the thermal characteristics of suspended MXene films, which can be further extended to the thermal properties of other 2D materials.

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.

Grain boundary and misorientation angle-dependent thermal transport in single-layer MoS2

Grain boundaries (GBs) are inevitable defects in large-area MoS₂ samples but they play a key role in their properties, however, the influence of grain misorientation on thermal transport has largely remained unknown. Here, the critical role of misorientation angle in thermal transport characteristics across 5|7 polar dislocation-dominated GBs in monolayer MoS₂ is explored using nonequilibrium molecular dynamics simulations. Results show that thermal transport characteristics of defective GBs are greatly dictated by the misorientation angle, with "U"-shaped thermal conductance as misorientation angle varying from around 5.06-52.26°, as well as by GB energy, 5|7 dislocation type and the grain size. Such unique thermal transport across GBs is primarily attributed to rising phonon-boundary softening and scattering with increasing dislocation density at GBs or GB energy, as well as an increase in localized phonon modes. The study establishes the fundamental relationship between GB and the thermal properties of single-layer MoS₂ and highlights the vital role of GBs in designing efficient thermoelectric and thermal management transition metal dichalcogenides.

A molecular dynamics simulation on the atomic mass sensor made of monolayer diamond

The recently synthesized monolayer diamond-diamane has proved to possess excellent mechanical and electrical properties, and it holds great potential in the field of nano-mass sensors. Herein, a molecular dynamics (MD) simulation is employed to systematically investigate the vibration response of the diamane nanoribbon (DNR) for the mass inspection. The results show that under different attached masses, the natural frequency of DNR is about three times of that of the bilayer graphene nanoribbon (BGNR) with the same size. The edge flatness of the DNR can be maintained during the vibration process, while the edge of the BGNR will warp in the initial state. Increasing the pre-strain can significantly increase the natural frequency of the DNR, leading to a higher response sensitivity of the DNR. In addition, the DNR has a higher mass resolution than the BGNR, and can detect smaller attached mass. The position of the attached mass in the resonator has a significant effect on the detection response. When the attached mass is near the center of the resonator, the frequency shift reaches the maximum value, and then it rapidly decreases to zero when the attached mass is close to the edge of DNR. Finally, the attached mass has no obvious effect on the quality factor of the DNR, and its value is stable between 10⁵and 10⁶orders of magnitude. The theoretical results demonstrate the accuracy of the MD results. The MD simulations reveal that the DNR has important implications as a resonant material for nano-mass sensor in the future.

Towards future physics and applications via two-dimensional material NEMS resonators

Two-dimensional materials (2Dm) offer a unique insight into the world of quantum mechanics including van der Waals (vdWs) interactions, exciton dynamics and various other nanoscale phenomena. 2Dm are a growing family consisting of graphene, hexagonal-Boron Nitride (h-BN), transition metal dichalcogenides (TMDs), monochalcogenides (MNs), black phosphorus (BP), MXenes and 2D organic crystals such as small molecules (e.g., pentacene, C8 BTBT, perylene derivatives, etc.) and polymers (e.g., COF and MOF, etc.). They exhibit unique mechanical, electrical, optical and optoelectronic properties that are highly enhanced as the surface to volume ratio increases, resulting from the transition of bulk to the few- to mono- layer limit. Such unique attributes include the manifestation of highly tuneable bandgap semiconductors, reduced dielectric screening, highly enhanced many body interactions, the ability to withstand high strains, ferromagnetism, piezoelectric and flexoelectric effects. Using 2Dm for mechanical resonators has become a promising field in nanoelectromechanical systems (NEMS) for applications involving sensors and condensed matter physics investigations. 2Dm NEMS resonators react with their environment, exhibit highly nonlinear behaviour from tension induced stiffening effects and couple different physics domains. The small size and high stiffness of these devices possess the potential of highly enhanced force sensitivities for measuring a wide variety of un-investigated physical forces. This review highlights current research in 2Dm NEMS resonators from fundamental physics and an applications standpoint, as well as presenting future possibilities using these devices.

Large-scale parallelization of nanomechanical mass spectrometry with weakly-coupled resonators

Nanomechanical mass spectrometry is a recent technological breakthrough that enables the real-time analysis of single molecules. In contraposition to its extreme mass sensitivity is a limited capture cross-section that can hinder measurements in a practical setting. Here we show that weak-coupling between devices in resonator arrays can be used in nanomechanical mass spectrometry to parallelize the measurement. This coupling gives rise to asymmetric amplitude peaks in the vibrational response of a single nanomechanical resonator of the array, which coincide with the natural frequencies of all other resonators in the same array. A rigorous theoretical model is derived that explains the physical mechanisms and describes the practical features of this parallelization. We demonstrate the significance of this parallelization through inertial imaging of analytes adsorbed to all resonators of an array, with the possibility of simultaneously detecting resonators placed at distances a hundred times larger than their own physical size.

Designing large-scale parallelization of nanomechanical array measurements remains elusive. Here, the authors propose weak-coupling between similar devices to evaluate the resonance frequencies of a whole resonator array with a single measurement.

Nonlinear Mode Coupling and One-to-One Internal Resonances in a Monolayer WS2 Nanoresonator

Nanomechanical resonators make exquisite force sensors due to their small footprint, low dissipation, and high frequencies. Because the lowest resolvable force is limited by ambient thermal noise, resonators are either operated at cryogenic temperatures or coupled to a high-finesse optical or microwave cavity to reach sub aN Hz^-1/2 sensitivity. Here, we show that operating a monolayer WS₂ nanoresonator in the strongly nonlinear regime can lead to comparable force sensitivities at room temperature. Cavity interferometry was used to transduce the nonlinear response of the nanoresonator, which was characterized by multiple pairs of 1:1 internal resonance. Some of the modes exhibited exotic line shapes due to the appearance of Hopf bifurcations, where the bifurcation frequency varied linearly with the driving force and forms the basis of the advanced sensing modality. The modality is less sensitive to the measurement bandwidth, limited only by the intrinsic frequency fluctuations, and therefore, advantageous in the detection of weak incoherent forces.

An ultrafast quantum thermometer from graphene quantum dots

We report an ultra-sensitive temperature sensor derived from graphene quantum dots (GQDs) embedded in a self-standing reduced graphene oxide (RGO) film. The GQDs are obtained as a natural derivative during synthesis of GO to RGO. A fundamental study on low temperature transport mechanisms reveals the applicability of temperature zone specific 'variable range hopping (VRH)' conduction models, i.e. Mott-VRH, Efros-Shklovskii-VRH and activation energy supported VRH. On the basis of transport behavior and confirmed by characterization analyses, the RGO film is modeled as GQD arrays where graphitic (sp2) domains behave as QDs and oxygenated (sp3) domains between interdots act as tunneling barriers. Temperature dependent resistance and current-voltage (I-V) characteristics indicate high sensitivity where sensor resistance changes by almost six orders of magnitude as the temperature is varied between 300 and 12 K. In convection mode, the developed temperature sensor shows a temperature coefficient of resistance (TCR) of ∼-1999% K-1 in the 300-77 K temperature range, which is much higher than the TCR values reported so far. Additionally, the sensor exhibits an extremely fast response (∼0.3 s) and recovery (0.8 s) time; and such high TCR leads to ultra high resolution of ∼ μK. The sensor shows excellent repeatability with negligible drift over several cycles. These studies are crucial for modern day thermal management and sensitive cryogenic applications.

Diamond nanothread based resonators: ultrahigh sensitivity and low dissipation

The recently synthesized ultrathin diamond nanothreads (NTHs) exhibit a variety of intriguing properties and are probably the most successful of many encouraging applications to be designed as resonators due to their ultrahigh sensitivity and low dissipation. Herein, we report via molecular dynamics that diamond nanothreads possess not only ultrahigh mass sensitivity but also a very high quality factor. On the one hand, the studied diamond nanothreads demonstrate an extreme mass resolution of ∼0.58 yg (1 yg = 10-24 g), which is almost one order of magnitude higher than that of carbon nanotubes (∼10 yg) with the same length. Moreover, the sensing performance of NTHs is highly tunable owing to their tailorable structures. On the other hand, NTHs exhibit a very low intrinsic energy dissipation and thus a high quality factor which is generally two times that of carbon nanotubes. These intriguing features suggest that diamond nanothreads could be highly attractive candidates for fabricating nano-sized mechanical resonators with outstanding performance.

Reduced Thermal Transport in the Graphene/MoS2/Graphene Heterostructure: A Comparison with Freestanding Monolayers

The thermal conductivity of the graphene-encapsulated MoS₂ (graphene/MoS₂/graphene) van der Waals heterostructure is determined along the armchair and zigzag directions with different twist angles between the layers using molecular dynamics (MD) simulations. The differences in the predictions relative to those of the monolayers are analyzed using the phonon power spectrum and phonon lifetimes obtained by spectral energy density analysis. The thermal conductivity of the heterostructure is predominantly isotropic. The out-of-plane phonons of graphene are suppressed because of the interaction between the adjacent layers that results in the reduced phonon lifetime and thermal conductivity relative to monolayer graphene. The occurrence of an additional nonzero phonon branch at the Γ point in the phonon dispersion curves of the heterostructure corresponds to the breathing modes resulting from stacking of the layers in the heterostructure. The thermal sheet conductance of the heterostructure being an order of magnitude larger than that of monolayer MoS₂, this van der Waals material is potentially suitable for efficient thermal packaging of photoelectronic devices. The interfacial thermal conductance of the graphene/MoS₂ bilayer as a function of the heat flow direction shows weak thermal rectification.

Room-Temperature Pressure-Induced Optically-Actuated Fabry-Perot Nanomechanical Resonator with Multilayer Graphene Diaphragm in Air

We demonstrated a miniature and in situ ~13-layer graphene nanomechanical resonator by utilizing a simple optical fiber Fabry-Perot (F-P) interferometric excitation and detection scheme. The graphene film was transferred onto the endface of a ferrule with a 125-μm inner diameter. In contrast to the pre-tension induced in membrane that increased quality (Q) factor to ~18.5 from ~3.23 at room temperature and normal pressure, the limited effects of air damping on resonance behaviors at 10⁻² and 10⁵ Pa were demonstrated by characterizing graphene F-P resonators with open and micro-air-gap cavities. Then in terms of optomechanical behaviors of the resonator with an air micro-cavity configuration using a polished ferrule substrate, measured resonance frequencies were increased to the range of 509–542 kHz from several kHz with a maximum Q factor of 16.6 despite the lower Knudsen number ranging from 0.0002 to 0.0006 in damping air over a relative pressure range of 0–199 kPa. However, there was the little dependence of Q on resonance frequency. Note that compared with the inferior F-P cavity length response to applied pressures due to interfacial air leakage, the developed F-P resonator exhibited a consistent fitted pressure sensitivity of 1.18 × 10⁵ kHz³/kPa with a good linearity error of 5.16% in the tested range. These measurements shed light on the pre-stress-dominated pressure-sensitive mechanisms behind air damping in in situ F-P resonant sensors using graphene or other 2D nanomaterials.

Strain-Modulated Electronic Structure and Infrared Light Adsorption in Palladium Diselenide Monolayer

Two-dimensional (2D) transition-metal dichalcogenides (TMDs) exhibit intriguing properties for both fundamental research and potential application in fields ranging from electronic devices to catalysis. Based on first-principles calculations, we proposed a stable form of palladium diselenide (PdSe₂) monolayer that can be synthesized by selenizing Pd(111) surface. It has a moderate band gap of about 1.10 eV, a small in-plane stiffness, and electron mobility larger than that of monolayer black phosphorus by more than one order. Additionally, tensile strain can modulate the band gap of PdSe₂ monolayer and consequently enhance the infrared light adsorption ability. These interesting properties are quite promising for application in electronic and optoelectronic devices.

Nonlinear intrinsic dissipation in single layer MoS2 resonators

Using dissipation models based on Akhiezer theory, we analyze the microscopic origin of nonlinearity in intrinsic loss of a single layer MoS₂.

The Effect of Viscous Air Damping on an Optically Actuated Multilayer MoS₂ Nanomechanical Resonator Using Fabry-Perot Interference

We demonstrated a multilayer molybdenum disulfide (MoS₂) nanomechanical resonator by using optical Fabry-Perot (F-P) interferometric excitation and detection. The thin circular MoS₂ nanomembrane with an approximate 8-nm thickness was transferred onto the endface of a ferrule with an inner diameter of 125 μm, which created a low finesse F-P interferometer with a cavity length of 39.92 μm. The effects of temperature and viscous air damping on resonance behavior of the resonator were investigated in the range of −10–80 °C. Along with the optomechanical behavior of the resonator in air, the measured resonance frequencies ranged from 36 kHz to 73 kHz with an extremely low inflection point at 20 °C, which conformed reasonably to those solved by previously obtained thermal expansion coefficients of MoS₂. Further, a maximum quality (Q) factor of 1.35 for the resonator was observed at 0 °C due to viscous dissipation, in relation to the lower Knudsen number of 0.0025~0.0034 in the tested temperature range. Moreover, measurements of Q factor revealed little dependence of Q on resonance frequency and temperature. These measurements shed light on the mechanisms behind viscous air damping in MoS₂, graphene, and other 2D resonators.

Nonlinear optical responses in two-dimensional transition metal dichalcogenide multilayer: WS2, WSe2, MoS2 and Mo 0.5 W0.5 S2

Synthetic two-dimensional transition metal dichalcogenides such as, tungsten disulphide (WS₂), tungsten diselenide (WSe₂), molybdenum disulphide (MoS₂) as well as mixed molybdenum tungsten disulphide (Mo_0.5W_0.5S₂) single crystals were grown by the chemical vapor transport method using halogens (bromine or chlorine) as transport agents. Multi- layer samples were cleaved from the single crystals, and their nonlinear optical (NLO) properties were obtained from both open aperture and closed aperture Z-scan measurements using a picosecond mode-locked Nd: YAG laser operating at a wavelength of 1064 nm, with pulse duration of 25 ps, and 20 Hz repetition rate. Both WS₂ and MoS₂ exhibited nonlinear saturable absorption (SA), whereas WSe₂ and Mo_0.5W_0.5S₂ showed nonlinear two-photon absorption (2PA). A large 2PA coefficient β as high as + 1.91x10^-8 cm/W was obtained for the Mo_0.5W_0.5S₂, and an index of refraction coefficient γ = -2.47x10^-9 cm²/W was obtained for the WSe₂ sample.

High Quality Factor Mechanical Resonators Based on WSe2 Monolayers

Suspended monolayer transition metal dichalcogenides (TMD) are membranes that combine ultralow mass and exceptional optical properties, making them intriguing materials for opto-mechanical applications. However, the low measured quality factor of TMD resonators has been a roadblock so far. Here, we report an ultrasensitive optical readout of monolayer TMD resonators that allows us to reveal their mechanical properties at cryogenic temperatures. We find that the quality factor of monolayer WSe2 resonators greatly increases below room temperature, reaching values as high as 1.6 × 10(4) at liquid nitrogen temperature and 4.7 × 10(4) at liquid helium temperature. This surpasses the quality factor of monolayer graphene resonators with similar surface areas. Upon cooling the resonator, the resonant frequency increases significantly due to the thermal contraction of the WSe2 lattice. These measurements allow us to experimentally study the thermal expansion coefficient of WSe2 monolayers for the first time. High Q-factors are also found in resonators based on MoS2 and MoSe2 monolayers. The high quality-factor found in this work opens new possibilities for coupling mechanical vibrational states to two-dimensional excitons, valley pseudospins, and single quantum emitters and for quantum opto-mechanical experiments based on the Casimir interaction.

Lattice Mismatch Dominant Yet Mechanically Tunable Thermal Conductivity in Bilayer Heterostructures

Heterostructures that are assembled by interfacing two-dimensional (2D) materials offer a unique platform for the emerging devices with unprecedented functions. The attractive functions in heterostructures that are usually absent and beyond the single layer 2D materials are largely affected by the inherent lattice mismatch between layers. Using nonequilibrium molecular dynamics simulations, we show that the phonon thermal transport in the graphene-MoS2 bilayer heterostructure is reduced by the lattice mismatch, and the reduction can be mitigated well by an external tension, weakening the effect of inherent mismatch-induced strain on thermal conductivity. Mechanical analysis in each layered component indicates that the external tension will alleviate the lattice mismatch-induced deformation. The phonon spectra are also softened by the applied tension with a significant shift of frequency from high to low modes. A universal theory is proposed to quantitatively predict the role of the lattice mismatch in thermal conductivity of various bilayer heterostructures and shows good agreement with simulations.

Mechanical strain effects on black phosphorus nanoresonators

We perform classical molecular dynamics simulations to investigate the effects of mechanical strain on single-layer black phosphorus nanoresonators at different temperatures. We find that the resonant frequency is highly anisotropic in black phosphorus due to its intrinsic puckered configuration, and that the quality factor in the armchair direction is higher than in the zigzag direction at room temperature. The quality factors are also found to be intrinsically larger than those in graphene and MoS2 nanoresonators. The quality factors can be increased by more than a factor of two by applying tensile strain, with uniaxial strain in the armchair direction being the most effective. However, there is an upper bound for the quality factor increase due to nonlinear effects at large strains, after which the quality factor decreases. The tension induced nonlinear effect is stronger along the zigzag direction, resulting in a smaller maximum strain for quality factor enhancement.

Piezoresistivity and Strain-induced Band Gap Tuning in Atomically Thin MoS2

Continuous tuning of material properties is highly desirable for a wide range of applications, with strain engineering being an interesting way of achieving it. The tuning range, however, is limited in conventional bulk materials that can suffer from plasticity and low fracture limit due to the presence of defects and dislocations. Atomically thin membranes such as MoS2 on the other hand exhibit high Young's modulus and fracture strength, which makes them viable candidates for modifying their properties via strain. The bandgap of MoS2 is highly strain-tunable, which results in the modulation of its electrical conductivity and manifests itself as the piezoresistive effect, whereas a piezoelectric effect was also observed in odd-layered MoS2 with broken inversion symmetry. This coupling between electrical and mechanical properties makes MoS2 a very promising material for nanoelectromechanical systems (NEMS). Here, we incorporate monolayer, bilayer, and trilayer MoS2 in a nanoelectromechanical membrane configuration. We detect strain-induced band gap tuning via electrical conductivity measurements and demonstrate the emergence of the piezoresistive effect in MoS2. Finite element method (FEM) simulations are used to quantify the band gap change and to obtain a comprehensive picture of the spatially varying bandgap profile on the membrane. The piezoresistive gauge factor is calculated to be -148 ± 19, -224 ± 19, and -43.5 ± 11 for monolayer, bilayer, and trilayer MoS2, respectively, which is comparable to state-of-the-art silicon strain sensors and 2 orders of magnitude higher than in strain sensors based on suspended graphene. Controllable modulation of resistivity in 2D nanomaterials using strain-induced bandgap tuning offers a novel approach for implementing an important class of NEMS transducers, flexible and wearable electronics, tunable photovoltaics, and photodetection.

Tuning the resonance properties of 2D carbon nanotube networks towards a mechanical resonator

The capabilities of the mechanical resonator-based nanosensors in detecting ultra-small mass or force shifts have driven a continuing exploration of the palette of nanomaterials for such application purposes. Based on large-scale molecular dynamics simulations, we have assessed the applicability of a new class of carbon nanomaterials for nanoresonator usage, i.e. the single-wall carbon nanotube (SWNT) network. It is found that SWNT networks inherit excellent mechanical properties from the constituent SWNTs, possessing a high natural frequency. However, although a high quality factor is suggested from the simulation results, it is hard to obtain an unambiguous Q-factor due to the existence of vibration modes in addition to the dominant mode. The nonlinearities resulting from these extra vibration modes are found to exist uniformly under various testing conditions including different initial actuations and temperatures. Further testing shows that these modes can be effectively suppressed through the introduction of axial strain, leading to an extremely high quality factor in the order of 10(9) estimated from the SWNT network with 2% tensile strain. Additional studies indicate that the carbon rings connecting the SWNTs can also be used to alter the vibrational properties of the resulting network. This study suggests that the SWNT network can be a good candidate for applications as nanoresonators.

A review on the flexural mode of graphene: lattice dynamics, thermal conduction, thermal expansion, elasticity and nanomechanical resonance

Single-layer graphene is so flexible that its flexural mode (also called the ZA mode, bending mode, or out-of-plane transverse acoustic mode) is important for its thermal and mechanical properties. Accordingly, this review focuses on exploring the relationship between the flexural mode and thermal and mechanical properties of graphene. We first survey the lattice dynamic properties of the flexural mode, where the rigid translational and rotational invariances play a crucial role. After that, we outline contributions from the flexural mode in four different physical properties or phenomena of graphene-its thermal conductivity, thermal expansion, Young's modulus and nanomechanical resonance. We explain how graphene's superior thermal conductivity is mainly due to its three acoustic phonon modes at room temperature, including the flexural mode. Its coefficient of thermal expansion is negative in a wide temperature range resulting from the particular vibration morphology of the flexural mode. We then describe how the Young's modulus of graphene can be extracted from its thermal fluctuations, which are dominated by the flexural mode. Finally, we discuss the effects of the flexural mode on graphene nanomechanical resonators, while also discussing how the essential properties of the resonators, including mass sensitivity and quality factor, can be enhanced.

In-plane and cross-plane thermal conductivities of molybdenum disulfide

We investigate the in-plane and cross-plane thermal conductivities of molybdenum disulfide (MoS2) using non-equilibrium molecular dynamics simulations. We find that the in-plane thermal conductivity of monolayer MoS2 is about 19.76 W mK(-1). Interestingly, the in-plane thermal conductivity of multilayer MoS2 is insensitive to the number of layers, which is in strong contrast to the in-plane thermal conductivity of graphene where the interlayer interaction strongly affects the in-plane thermal conductivity. This layer number insensitivity is attributable to the finite energy gap in the phonon spectrum of MoS2, which makes the phonon-phonon scattering channel almost unchanged with increasing layer number. For the cross-plane thermal transport, we find that the cross-plane thermal conductivity of multilayer MoS2 can be effectively tuned by applying cross-plane strain. More specifically, a 10% cross-plane compressive strain can enhance the thermal conductivity by a factor of 10, while a 5% cross-plane tensile strain can reduce the thermal conductivity by 90%. Our findings are important for thermal management in MoS2 based nanodevices and for thermoelectric applications of MoS2.

The strain rate effect on the buckling of single-layer MoS2

The Euler buckling theory states that the buckling critical strain is an inverse quadratic function of the length for a thin plate in the static compression process. However, the suitability of this theory in the dynamical process is unclear, so we perform molecular dynamics simulations to examine the applicability of the Euler buckling theory for the fast compression of the single-layer MoS₂. We find that the Euler buckling theory is not applicable in such dynamical process, as the buckling critical strain becomes a length-independent constant in the buckled system with many ripples. However, the Euler buckling theory can be resumed in the dynamical process after restricting the theory to an individual ripple in the buckled structure.

Broadband ultrafast nonlinear absorption and nonlinear refraction of layered molybdenum dichalcogenide semiconductors

A series of layered molybdenum dichalcogenides, i.e., MoX₂ (X = S, Se and Te), were prepared in cyclohexyl pyrrolidinone by a liquid-phase exfoliation technique. The high quality of the two-dimensional nanostructures was verified by transmission electron microscopy and absorption spectroscopy. Open- and closed-aperture Z-scans were employed to study the nonlinear absorption and nonlinear refraction of the MoX₂ dispersions, respectively. All the three-layered nanostructures exhibit prominent ultrafast saturable absorption (SA) for both femtosecond (fs) and picosecond (ps) laser pulses over a broad wavelength range from the visible to the near infrared. While the dispersions treated with low-speed centrifugation (1500 rpm) have an SA response, and the MoS₂ and MoSe₂ dispersions after higher speed centrifugation (10,000 rpm) possess two-photon absorption for fs pulses at 1030 nm, which is due to the significant reduction of the average thickness of the nanosheets; hence, the broadening of band gap. In addition, all dispersions show obvious nonlinear self-defocusing for ps pulses at both 1064 nm and 532 nm, resulting from the thermally-induced nonlinear refractive index. The versatile ultrafast nonlinear properties imply a huge potential of the layered MoX2 semiconductors in the development of nanophotonic devices, such as mode-lockers, optical limiters, optical switches, etc.

The buckling of single-layer MoS2 under uniaxial compression

Molecular dynamics simulations are performed to investigate the buckling of single-layer MoS2 under uniaxial compression. The strain rate is found to have an important effect on the critical buckling strain, where higher strain rate leads to larger critical strain. The critical strain is almost temperature-independent for [Formula: see text] K, and it increases with increasing temperature for [Formula: see text] K owing to the thermal vibration assisted healing mechanism on the buckling deformation. The length-dependence of the critical strain from our simulations is in good agreement with the prediction of the Euler buckling theory.

Phonon bandgap engineering of strained monolayer MoS₂

The phonon band structure of monolayer MoS₂ is characteristic of a large energy gap between acoustic and optical branches, which protects the vibration of acoustic modes from being scattered by optical phonon modes. Therefore, the phonon bandgap engineering is of practical significance for the manipulation of phonon-related mechanical or thermal properties in monolayer MoS₂. We perform both phonon analysis and molecular dynamics simulations to investigate the tension effect on the phonon bandgap and the compression induced instability of the monolayer MoS₂. Our key finding is that the phonon bandgap can be narrowed by the uniaxial tension, and is completely closed at ε = 0.145; while the biaxial tension only has a limited effect on the phonon bandgap. We also demonstrate the compression induced buckling for the monolayer MoS₂. The critical strain for buckling is extracted from the band structure analysis of the flexure mode in the monolayer MoS₂ and is further verified by molecular dynamics simulations and the Euler buckling theory. Our study illustrates the uniaxial tension as an efficient method for manipulating the phonon bandgap of the monolayer MoS₂, while the biaxial compression as a powerful tool to intrigue buckling in the monolayer MoS₂.

Embracing structural nonidealities and asymmetries in two-dimensional nanomechanical resonators

Mechanical exfoliation is a convenient and effective approach to deriving two-dimensional (2D) nanodevices from layered materials; but it is also generally perceived as unpreferred as it often yields devices with structural irregularities and nonidealities. Here we show that such nonidealities can lead to new and engineerable features that should be embraced and exploited. We measure and analyze high frequency nanomechanical resonators based on exfoliated 2D molybdenum disulfide (MoS2) structures, and focus on investigating the effects of structural nonidealities and asymmetries on device characteristics and performance. In high and very high frequency (HF/VHF) vibrating MoS2 devices based on diaphragms of ~2-5 μm in size, structural nonidealities in shape, boundary, and geometric symmetry all appear not to compromise device performance, but lead to robust devices exhibiting new multimode resonances with characteristics that are inaccessible in their 'ideal' counterparts. These results reveal that the seemingly irregular and nonideal 2D structures can be exploited and engineered for new designs and functions.