Giant Tunable Mechanical Nonlinearity in Graphene-Silicon Nitride Hybrid Resonator

Self-Injection Locked and Phase Offset-Free Micromechanical Frequency Combs

Pure mechanical frequency combs attracted a lot of attention recently due to the intriguing nonlinear dynamics and potential of miniatured precision timekeeping but are currently limited by narrow spectra and missing frequency locking physics. In this Letter, we report the design and experiment of a self-injection locked micromechanical frequency comb that is further intrinsically immune to phase offset. We show that by tuning the pump frequency of a pair of nonlinearly coupled flexural and torsional oscillations, self-injection locking could be achieved via aligning the comb teeth from neighboring harmonic clusters, leading to decade-wide cascading of hundreds of equidistant teeth. Inside the injection locking region, the stability of the comb spacing and the phase noise are significantly improved. Moreover, the phase offset in the temporal signal also disappears because all comb lines are locked as integer multiples of the comb spacing and the first tooth is locked to the d.c. frequency due to the comb origination from harmonics. The observation of self-injection locking and zero phase offset in mechanical frequency combs greatly promotes their value for precision applications.

NEMS generated electromechanical frequency combs

This paper presents a novel technique for low-power generation of frequency combs (FC) over a wide frequency range. It leverages modal interactions between electrical and mechanical resonators in electrostatic NEMS operating in air to provide a simple architecture for FC generators. A biased voltage signal drives the electrical resonator at resonance which is set to match an integer submultiple of twice the mechanical resonator's resonance. Experimental results demonstrate that the NEMS displacement exhibit more than 150 equidistant peaks in the case of a 2:1 modal interaction and more than 60 equidistant peaks in the case of a 1:1 modal interaction. In both cases, the Free Spectral Range (FSR) was equal to the mechanical resonance frequency. Comparison between the FCs generated by the 2:1 and 1:1 modal interactions demonstrate the superiority of the former in terms of bandwidth and stability. The superior phase coherence of the FC generated via the 2:1 modal interaction was demonstrated via time-domain analysis. Our technique has the flexibility to generate multiple frequency combs and to fine-tune their FSR depending on the number of mechanical modes accessible to and the order of the activated modal interaction. It can be integrated into portable devices and is well aligned with modern miniaturization technology.

Generation of Soliton Frequency Combs in NEMS

In this study, we present an innovative approach leveraging combination internal resonances within a NEMS platform to generate mechanical soliton frequency combs (FCs) spanning a broad spectrum. In the time domain, the FCs take the form of a periodic train of narrow pulses, a highly coveted phenomenon within the realm of nonlinear wave-matter interactions. Our method relies on an intricate interaction among multiple vibration modes of a bracket-nanocantilever enabled by the strong nonlinearity of the electrostatic field. Through numerical simulation and experimental validation, we demonstrate that by amplifying the motions of the NEMS with the external electrostatic forcing tuned to excite the superharmonic resonance of order-n of the fundamental mode and exploiting combination internal resonances, we can generate multiple stable localized mechanical wave packets with different lobe sizes embodying soliton states I and II. This represents a significant breakthrough with profound implications for quantum computing and metrology.

Mapping of Vibrational Modes Revealing a Strong and Tunable Coupling in Two Juxtaposed 3R-WSe2 Nanodrums

Two-dimensional (2D) material resonators have emerged as promising platforms for advanced nanomechanical applications due to their exceptional mechanical properties, tunability, and nonlinearities. We explored the strong mechanical mode coupling between two adjacent 3R-WSe2 nanodrums at room temperature. Combining a piezoelectric material, as noncentrosymmetric 3R-WSe2, and vibration manipulation is the building block for phononic experiments with 2D materials. By strategically placing gate grids beneath each resonator and mapping the spatial distribution of these modes, we demonstrate the ability to transit between localized modes in individual membranes to delocalized, strongly coupled modes that span the entire suspended region. The coherent coupling is strongly tunable with simple gate voltage, and remarkable resonance splitting was achieved, corresponding to up to 5% of the vibration frequency. These results showcase the potential of 2D material resonators for efficient information exchange, paving the way for novel applications in quantum technologies and nanoscale sensing.

Coupling of MoS_{2} Excitons with Lattice Phonons and Cavity Vibrational Phonons in Hybrid Nanobeam Cavities

We report resonant Raman spectroscopy of neutral excitons X^{0} and intravalley trions X^{-} in hBN-encapsulated MoS_{2} monolayer embedded in a nanobeam cavity. By temperature tuning the detuning between Raman modes of MoS_{2} lattice phonons and X^{0}/X^{-} emission peaks, we probe the mutual coupling of excitons, lattice phonons and cavity vibrational phonons. We observe an enhancement of X^{0}-induced Raman scattering and a suppression for X^{-}-induced, and explain our findings as arising from the tripartite exciton-phonon-phonon coupling. The cavity vibrational phonons provide intermediate replica states of X^{0} for resonance conditions in the scattering of lattice phonons, thus enhancing the Raman intensity. In contrast, the tripartite coupling involving X^{-} is found to be much weaker, an observation explained by the geometry-dependent polarity of the electron and hole deformation potentials. Our results indicate that phononic hybridization between lattice and nanomechanical modes plays a key role in the excitonic photophysics and light-matter interaction in 2D-material nanophotonic systems.

Mechanical overtone frequency combs

Mechanical frequency combs are poised to bring the applications and utility of optical frequency combs into the mechanical domain. So far, their main challenge has been strict requirements on drive frequencies and power, which complicate operation. We demonstrate a straightforward mechanism to create a frequency comb consisting of mechanical overtones (integer multiples) of a single eigenfrequency, by monolithically integrating a suspended dielectric membrane with a counter-propagating optical trap. The periodic optical field modulates the dielectrophoretic force on the membrane at the overtones of a membrane's motion. These overtones share a fixed frequency and phase relation, and constitute a mechanical frequency comb. The periodic optical field also creates an optothermal parametric drive that requires no additional power or external frequency reference. This combination of effects results in an easy-to-use mechanical frequency comb platform that requires no precise alignment, no additional feedback or control electronics, and only uses a single, mW continuous wave laser beam. This highlights the overtone frequency comb as the straightforward future for applications in sensing, metrology and quantum acoustics.

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.

Nano-Optomechanical Resonators Based on Suspended Graphene for Thermal Stress Sensing

Nanomechanical resonators made from suspended graphene combine the properties of ultracompactness and ultrahigh detection sensitivity, making them interesting devices for sensing applications. However, nanomechanical systems can be affected by membrane stress. The present work developed an optomechanical resonator for thermal stress sensing. The proposed resonator consists of a section of hollow core fiber (HCF) and a trampoline graphene-Au membrane. An all-optical system that integrated optical excitation and optical detection was applied. Then, the resonance frequency of the resonator was obtained through this all-optical system. In addition, this system and the resonator were used to detect the membrane's built-in stress, which depended on the ambient temperature, by monitoring the resonance frequency shift. The results verified that the temperature-induced thermal effect had a significant impact on membrane stress. Temperature sensitivities of 2.2646 kHz/°C and 2.3212 kHz/°C were obtained when the temperature rose and fell, respectively. As such, we believe that this device will be beneficial for the quality monitoring of graphene mechanical resonators.

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.

Symmetry-Breaking-Induced Frequency Combs in Graphene Resonators

Nonlinearities are inherent to the dynamics of two-dimensional materials. Phenomena-like intermodal coupling already arise at amplitudes of only a few nanometers, and a range of unexplored effects still awaits to be harnessed. Here, we demonstrate a route for generating mechanical frequency combs in graphene resonators undergoing symmetry-breaking forces. We use electrostatic force to break the membrane's out-of-plane symmetry and tune its resonance frequency toward a one-to-two internal resonance, thus achieving strong coupling between two of its mechanical modes. When increasing the drive level, we observe splitting of the fundamental resonance peak, followed by the emergence of a frequency comb regime. We attribute the observed physics to a nonsymmetric restoring potential and show that the frequency comb regime is mediated by Neimark bifurcation of the periodic solution. These results demonstrate that mechanical frequency combs and chaotic dynamics in 2D material resonators can emerge near internal resonances due to symmetry-breaking.

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.

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.