Real-time vibrations of a carbon nanotube

Carbon-Based Nanomaterials Decorated Electrospun Nanofibers in Biosensors: A Review

Nanomaterials have revolutionized scientific research due to their exceptional physical and chemical capabilities. Carbon-based nanomaterials such as graphene and its derivates have excellent electrical, optical, thermal, physical, and chemical properties that have made them indispensable in several industries worldwide, including medicine, electronics, and energy. By incorporating carbon-based nanomaterials as nanofillers in electrospun nanofibers (ESNFs), smoother and highly conductive nanofibers can be achieved that possess a large surface area and porosity. This approach provides a superior alternative to traditional materials in the development of improved biosensors. Carbon-based ESNFs, among the most exciting new-generation materials, have many applications, including filtration, pharmaceuticals, biosensors, and membranes. The electrospinning technique is a highly efficient and cost-effective method for producing desired nanofibers compared to other methods. Various types of natural and synthetic organic polymers have been successfully utilized in solution electrospinning to produce nanofibers directly. To create diagnostics devices, various biomolecules like antibodies, enzymes, aptamers, ligands, and even cells can be bound to the surface of nanofibers. Electrospun nanofibers can serve as an immobilization matrix to create a biofunctional surface. Thus, biosensors with desired features can be produced in this way. This study comprehensively reviews biosensors that integrate nanodiamonds, fullerenes, carbon nanotubes, graphene oxide, and carbon dots into electrospun nanofibers.

Dissipative optomechanics in high-frequency nanomechanical resonators

The coherent transduction of information between microwave and optical domains is a fundamental building block for future quantum networks. A promising way to bridge these widely different frequencies is using high-frequency nanomechanical resonators interacting with low-loss optical modes. State-of-the-art optomechanical devices rely on purely dispersive interactions that are enhanced by a large photon population in the cavity. Additionally, one could use dissipative optomechanics, where photons can be scattered directly from a waveguide into a resonator hence increasing the degree of control of the acousto-optic interplay. Hitherto, such dissipative optomechanical interaction was only demonstrated at low mechanical frequencies, precluding prominent applications such as the quantum state transfer between photonic and phononic domains. Here, we show the first dissipative optomechanical system operating in the sideband-resolved regime, where the mechanical frequency is larger than the optical linewidth. Exploring this unprecedented regime, we demonstrate the impact of dissipative optomechanical coupling in reshaping both mechanical and optical spectra. Our figures represent a two-order-of-magnitude leap in the mechanical frequency and a tenfold increase in the dissipative optomechanical coupling rate compared to previous works. Further advances could enable the individual addressing of mechanical modes and help mitigate optical nonlinearities and absorption in optomechanical devices.

Analysis of the vibrational characteristics of diamane nanosheet based on the Kirchhoff plate model and atomistic simulations

Single layer diamond-diamane, has been reported with excellent mechanical properties. In this work, molecular dynamics (MD) simulation and Kirchhoff plate model are utilized to investigate the vibrational characteristics of diamane sheets. The mechanical parameters of diamane sheets, including bending stiffness, Young's modulus, Poisson's ratio and coefficient of thermal expansion, are calibrated by using MD simulations. The natural frequencies and corresponding modal shapes of the diamane sheets predicted by the Kirchhoff plate model agree well with that obtained from the MD simulations. It is found that the edges exert marginal effect on the modal shapes when free boundary conditions are applied. Additionally, the Kirchhoff plate model considering the thermal expansion provides reasonable prediction for the natural frequencies of the diamane sheets with all boundary clamped under varying temperatures. This study offers valuable insights into the vibrational properties of diamane sheets, from both a simulation and theoretical standpoint. The findings would be beneficial for the design of nanoscale mechanical resonators utilizing these novel carbon materials.

Radiation Pressure Backaction on a Hexagonal Boron Nitride Nanomechanical Resonator

Hexagonal boron nitride (hBN) is a van der Waals material with excellent mechanical properties hosting quantum emitters and optically active spin defects, with several of them being sensitive to strain. Establishing optomechanical control of hBN will enable hybrid quantum devices that combine the spin degree of freedom with the cavity optomechanical toolbox. In this Letter, we report the first observation of radiation pressure backaction at telecom wavelengths with a hBN drum-head mechanical resonator. The thermomechanical motion of the resonator is coupled to the optical mode of a high finesse fiber-based Fabry-Pérot microcavity in a membrane-in-the-middle configuration. We are able to resolve the optical spring effect and optomechanical damping with a single photon coupling strength of g₀/2π = 1200 Hz. Our results pave the way for tailoring the mechanical properties of hBN resonators with light.

Constitutive Modeling of Mechanical Behaviors of Carbon-Based CNTs and GSs, and Their Sensing Applications as Nanomechanical Resonators: A Review

Carbon-based nanomaterials, including carbon nanotubes (CNTs) and graphene sheets (GSs), have garnered considerable research attention owing to their unique mechanical, physical, and chemical properties compared with traditional materials. Nanosensors are sensing devices with sensing elements made of nanomaterials or nanostructures. CNT- and GS-based nanomaterials have been proved to be very sensitive nanosensing elements, being used to detect tiny mass and force. In this study, we review the developments in the analytical modeling of mechanical behavior of CNTs and GSs, and their potential applications as next-generation nanosensing elements. Subsequently, we discuss the contributions of various simulation studies on theoretical models, calculation methods, and mechanical performance analyses. In particular, this review intends to provide a theoretical framework for a comprehensive understanding of the mechanical properties and potential applications of CNTs/GSs nanomaterials as demonstrated by modeling and simulation methods. According to analytical modeling, nonlocal continuum mechanics pose small-scale structural effects in nanomaterials. Thus, we overviewed a few representative studies on the mechanical behavior of nanomaterials to inspire the future development of nanomaterial-based sensors or devices. In summary, nanomaterials, such as CNTs and GSs, can be effectively utilized for ultrahigh-sensitivity measurements at a nanolevel resolution compared to traditional materials.

Beating thermal noise in a dynamic signal measurement by a nanofabricated cavity optomechanical sensor

Thermal fluctuations often impose both fundamental and practical measurement limits on high-performance sensors, motivating the development of techniques that bypass the limitations imposed by thermal noise outside cryogenic environments. Here, we theoretically propose and experimentally demonstrate a measurement method that reduces the effective transducer temperature and improves the measurement precision of a dynamic impulse response signal. Thermal noise-limited, integrated cavity optomechanical atomic force microscopy probes are used in a photothermal-induced resonance measurement to demonstrate an effective temperature reduction by a factor of ≈25, i.e., from room temperature down as low as ≈12 K, without cryogens. The method improves the experimental measurement precision and throughput by >2×, approaching the theoretical limit of ≈3.5× improvement for our experimental conditions. The general applicability of this method to dynamic measurements leveraging thermal noise-limited harmonic transducers will have a broad impact across a variety of measurement platforms and scientific fields.

Direct Observation of Thermal Vibration Modes Using Frequency-Selective Electron Microscopy

Thermal vibration properties of nanometer-scale objects are critical for their application in devices such as nanomechanical resonators. An imaging method has been developed which allows the direct visualization of higher-order thermal vibration modes at room temperature, which have so far been inaccessible to observation due to their subangstrom amplitudes and the much stronger overlapped first mode. This technique, combining aberration-corrected scanning transmission electron microscopy with broad-band signal acquisition in the time domain, can display the amplitude distribution of several thermal vibration modes simultaneously by selecting specific frequency windows. This is showcased by mapping the first six thermal vibration modes of a singly clamped nanowire and comparing them to natural vibration mode profiles obtained by finite element calculations. This implementation furthers our understanding of the collective Brownian motion of nanostructures and extends the analysis capabilities of electron microscopy.

Can Linear Conjugated Polymers Form Stable Helical Structures on the Carbon Nanotubes?

The formation mechanism of ordered helical structures of conjugated polymers wrapping onto single-walled carbon nanotubes (SWCNTs) has been full of controversy in recent decades. A formation mechanism is proposed for the linear conjugated polymers wrapping around SWCNTs that the formation of helical structures is dependent on the orientation competition between backbone segments and side groups via transmission electron microscopy observations and molecular dynamics simulations. Results show that the conjugated polymers cannot always form stable helical structures, even if they have the capability to form a stable helix. In fact, only part of polymer segments presents a stable helix on the SWCNTs for the internal rotation in polymer deformations. Furthermore, a design framework is proposed to choose specific conjugated homopolymers and copolymers which can form helical structures on the SWCNTs.

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.

A Universal Pick-and-Place Assembly for Nanowires

With the introduction of techniques to grow highly functional nanowires of exotic materials and demonstrations of their potential in new applications, techniques for depositing nanowires on functional platforms have been an area of active interest. However, difficulties in handling individual nanowires with high accuracy and reliability have so far been a limiting factor in large-scale integration of high-quality nanowires. Here, a technique is demonstrated to transfer single nanowires reliably on virtually any platform, under ambient conditions. Functional nanowires of InP, AlGaAs, and GeTe on various patterned structures such as electrodes, nanophotonic devices, and even ultrathin transmission electron microscopy (TEM) membranes are transferred. It is shown that the versatility of this technique further enables to perform on-chip nano-optomechanical measurements of an InP nanowire for the first time via evanescent field coupling. Thus, this technique facilitates effortless integration of single nanowires into applications that were previously seen as cumbersome or even impractical, spanning a wide range from TEM studies to in situ electrical, optical, and mechanical characterization.

Dissipative Acousto-optic Interactions in Optical Microcavities

We propose and demonstrate experimentally the strong dissipative acousto-optic interaction between a suspended vibrating microfiber and a whispering-gallery microcavity. On the one hand, the dissipative response driven by an external stimulus of acoustic waves is found to be stronger than the dispersive response by 2 orders of magnitude. On the other hand, dead points emerge with the zero dissipative response at certain parameters, promising the potentials in physical sensing such as precise measurements of magnetic field and temperature. The strong dissipative acousto-optic interaction is then explored for ultrasensitive detection of broadband acoustic waves. A noise equivalent pressure as low as 0.81 Pa at 140 kHz in air is demonstrated experimentally, insensitive to cavity Q factors and does not rely on mechanical resonances.

Optical computing of quantum revivals

Interference is the mechanism through which waves can be structured into the most fascinating patterns. While for sensing, imaging, trapping, or in fundamental investigations, structured waves play nowadays an important role and are becoming the subject of many interesting studies. Using a coherent optical field as a probe, we show how to structure light into distributions presenting collapse and revival structures in its wavefront. These distributions are obtained from the Fourier spectrum of an arrangement of aperiodic diffracting structures. Interestingly, the resulting interference may present quasiperiodic structures of diffraction peaks on a number of distance scales, even though the diffracting structure is not periodic. We establish an analogy with revival phenomena in the evolution of quantum mechanical systems and illustrate this computation numerically and experimentally, obtaining excellent agreement with the proposed theory.

Atomic-number (Z)-correlated atomic sizes for deciphering electron microscopic molecular images

Atomic resolution transmission electron microscopy (TEM) has opened up a new era of molecular science by providing atomic video images of dynamic motions of single organic and inorganic molecules. However, the images often look different from the images of molecular models, because these models are designed to visualize the electronic properties of the molecule instead of nuclear electrostatic potentials that are felt by the e-beam in TEM imaging. Here, we propose a molecular model that reproduces TEM images using atomic radii correlated to atomic number (Z). The model serves to provide a priori a useful idea of how a single molecule, molecular assemblies, and thin crystals of organic or inorganic materials look in TEM.

With the advent of atomic resolution transmission electron microscopy (AR-TEM) achieving sub-Ångstrom image resolution and submillisecond time resolution, an era of cinematic molecular science where chemists can visually study the time evolution of molecular motions and reactions at atomistic precision has arrived. However, the appearance of experimental TEM images often differs greatly from that of conventional molecular models, and the images are difficult to decipher unless we know in advance the structure of the specimen molecules. The difference arises from the fundamental design of the molecular models that represent atomic connectivity and/or the electronic properties of molecules rather than the nuclear charge of atoms and electrostatic potentials that are felt by the e-beam in TEM imaging. We found a good correlation between the atomic number (Z) and the atomic size seen in TEM images when we consider shot noise in digital images. We propose Z-correlated (ZC) atomic radii for modeling AR-TEM images of single molecules and ultrathin crystals with which we can develop a good estimate of the molecular structure from the TEM image much more easily than with conventional molecular models. Two parameter sets were developed for TEM images recorded under high-noise (ZC_HN) and low-noise (ZC_LN) conditions. The molecular models will stimulate the imaginations of chemists planning to use AR-TEM for their research.

Persistent Nonlinear Phase-Locking and Nonmonotonic Energy Dissipation in Micromechanical Resonators

Many nonlinear systems are described by eigenmodes with amplitude-dependent frequencies, interacting strongly whenever the frequencies become commensurate at internal resonances. Fast energy exchange via the resonances holds the key to rich dynamical behavior, such as time-varying relaxation rates and signatures of nonergodicity in thermal equilibrium, revealed in the recent experimental and theoretical studies of micro- and nanomechanical resonators. However, a universal yet intuitive physical description for these diverse and sometimes contradictory experimental observations remains elusive. Here we experimentally reveal persistent nonlinear phase-locked states occurring at internal resonances and demonstrate that they are essential for understanding the transient dynamics of nonlinear systems with coupled eigenmodes. The measured dynamics of a fully observable micromechanical resonator system are quantitatively described by the lower-frequency mode entering, maintaining, and exiting a persistent phase-locked period-tripling state generated by the nonlinear driving force exerted by the higher-frequency mode. This model describes the observed phase-locked coherence times, the direction and magnitude of the energy exchange, and the resulting nonmonotonic mode energy evolution. Depending on the initial relative phase, the system selects distinct relaxation pathways, either entering or bypassing the locked state. The described persistent phase locking is not limited to particular frequency fractions or types of nonlinearities and may advance nonlinear resonator systems engineering across physical domains, including photonics as well as nanomechanics.

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.

Nanomechanical Measurement of the Brownian Force Noise in a Viscous Liquid

We study the frequency spectrum of the thermal force giving rise to Brownian motion of a nanomechanical beam resonator in a viscous liquid. In the first set of experiments, we measure the power spectral density (PSD) of the position fluctuations of the resonator around its fundamental mode at its center. Then, we measure the frequency-dependent linear response of the resonator, again at its center, by driving it with a harmonic force that couples well to the fundamental mode. These two measurements allow us to determine the PSD of the Brownian force noise acting on the structure in its fundamental mode. The PSD of the force noise from multiple resonators spanning a broad frequency range displays a "colored spectrum" and follows the dissipation of a blade oscillating in a viscous liquid-by virtue of the fluctuation-dissipation theorem of statistical mechanics.

Heat diffusion-related damping process in a highly precise coarse-grained model for nonlinear motion of SWCNT

Second sound and heat diffusion in single-walled carbon nanotubes (SWCNT) are well-known phenomena which is related to the high thermal conductivity of this material. In this paper, we have shown that the heat diffusion along the tube axis affects the macroscopic motion of SWCNT and adapting this phenomena to coarse-grained (CG) model can improve the precision of the coarse-grained molecular dynamics (CGMD) exceptionally. The nonlinear macroscopic motion of SWCNT in the free thermal vibration condition in adiabatic environment is demonstrated in the most simplified version of CG modeling as maintaining finite temperature and total energy with suggested dissipation process derived from internal heat diffusion. The internal heat diffusion related to the cross correlated momentum from different potential energy functions is considered, and it can reproduce the nonlinear dynamic nature of SWCNTs without external thermostatting in CG model. Memory effect and thermostat with random noise distribution are not included, and the effect of heat diffusion on memory effect is quantified through Mori-Zwanzig formalism. This diffusion shows perfect syncronization of the motion between that of CGMD and MD simulation, which is started with initial conditions from the molecular dynamics (MD) simulation. The heat diffusion related to this process has shown the same dispersive characteristics to second wave in SWCNT. This replication with good precision indicates that the internal heat diffusion process is the essential cause of the nonlinearity of the tube. The nonlinear dynamic characteristics from the various scale of simple beads systems are examined with expanding its time step and node length.

Effects of curvature on the propagation of undulatory waves in lower dimensional elastic materials

The mechanics of lower dimensional elastic structures depends strongly on the geometry of their stress-free state. Elastic deformations separate into in-plane stretching and lower energy out-of-plane bending deformations. For elastic structures with a curved stress-free state, these two elastic modes are coupled within linear elasticity. We investigate the effect of that curvature-induced coupling on wave propagation in lower dimensional elastic structures, focusing on the simplest example-a curved elastic rod in two dimensions. We focus only on the geometry-induced coupling between bending and longitudinal (in-plane) strain that is common to both rods in two dimensions and to elastic shells. We find that the dispersion relation of the waves becomes gapped in the presence of finite curvature; bending modes are absent below a frequency proportional to the curvature of the rod. By studying the scattering of undulatory waves off regions of uniform curvature, we find that undulatory waves with frequencies in the gap associated with the curved region tunnel through that curved region via conversion into compression waves. These results should be directly applicable to the spectrum and spatial distribution of phonon modes in a number of curved rod-like elastic solids, including carbon nanotubes and biopolymer filaments.

Fundamental limits and optimal estimation of the resonance frequency of a linear harmonic oscillator

All physical oscillators are subject to thermodynamic and quantum perturbations, fundamentally limiting measurement of their resonance frequency. Analyses assuming specific ways of estimating frequency can underestimate the available precision and overlook unconventional measurement regimes. Here we derive a general, estimation-method-independent Cramer Rao lower bound for a linear harmonic oscillator resonance frequency measurement uncertainty, seamlessly accounting for the quantum, thermodynamic and instrumental limitations, including Fisher information from quantum backaction- and thermodynamically-driven fluctuations. We provide a universal and practical maximum-likelihood frequency estimator reaching the predicted limits in all regimes, and experimentally validate it on a thermodynamically-limited nanomechanical oscillator. Low relative frequency uncertainty is obtained for both very high bandwidth measurements (≈ 10-5 for τ = 30 μs ) and measurements using thermal fluctuations alone (<10-6). Beyond nanomechanics, these results advance frequency-based metrology across physical domains.

Quasinormal-Mode Perturbation Theory for Dissipative and Dispersive Optomechanics

Despite the several novel features arising from the dissipative optomechanical coupling, such effect remains vastly unexplored due to the lack of a simple formalism that captures non-Hermiticity in the engineering of optomechanical systems. In this Letter, we show that quasinormal-mode-based perturbation theory is capable of correctly predicting both dispersive and dissipative optomechanical couplings. We validate our model through simulations and also by comparison with experimental results reported in the literature. Finally, we apply this formalism to plasmonic systems, used for molecular optomechanics, where strong dissipative coupling signatures in the amplification of vibrational modes could be observed.

Whispering-Gallery Sensors

Optical whispering-gallery mode (WGM) microresonators, confining resonant photons in a microscale volume for long periods of time, strongly enhance light-matter interactions, making them an ideal platform for photonic sensors. One of the features of WGM sensors is their capability to respond to environmental perturbations that influence the optical mode distribution. The exceptional sensitivity of WGM devices, coupled with the diversity in their structures and the ease of integration with existing infrastructures, such as conventional chip-based technologies, has catalyzed the development of WGM sensors for a broad range of analytes. WGM sensors have been developed for multiplexed detection of clinically relevant biomolecules while also being adapted for the analysis of single-protein interactions. They have been used for the detection of materials in different phases and forms, including gases, liquids, and chemicals. Furthermore, WGM sensors have been used for a wide variety of field-based sensing applications, including electric field, magnetic field, force, pressure, and temperature. WGM sensors hold great potential for applications in life and environmental sciences. They are expected to meet the ever-increasing demand in sensor networks, the Internet of Things, and real-time health monitoring. Here we review the mechanisms, structures, parameters, and recent advances of WGM microsensors and discuss the future of this exciting research field.

Metallic Carbon Nanotube Nanocavities as Ultracompact and Low-loss Fabry-Perot Plasmonic Resonators

Plasmonic resonators enable deep subwavelength manipulation of light matter interactions and have been intensively studied both in fundamental physics as well as for potential technological applications. While various metallic nanostructures have been proposed as plasmonic resonators, their performances are rather limited at mid- and far-infrared wavelengths. Recently, highly confined and low-loss Luttinger liquid plasmons in metallic single-walled carbon nanotubes (SWNTs) have been observed at infrared wavelengths. Here, we tailor metallic SWNTs into ultraclean nanocavities by advanced scanning probe lithography and investigate plasmon modes in these individual nanocavities by infrared nanoimaging. The dependence of mode evolutions on cavity length and excitation wavelength can be captured by a Fabry-Perot resonator model of a plasmon nanowaveguide terminated by highly reflective ends. Plasmonic resonators based on SWNT nanocavities approach the ultimate plasmon confinement limit and open the door to the strong light-matter coupling regime, which may enable various nanophotonic applications.

Quantum capacitance mediated carbon nanotube optomechanics

Cavity optomechanics allows the characterization of a vibration mode, its cooling and quantum manipulation using electromagnetic fields. Regarding nanomechanical as well as electronic properties, single wall carbon nanotubes are a prototypical experimental system. At cryogenic temperatures, as high quality factor vibrational resonators, they display strong interaction between motion and single-electron tunneling. Here, we demonstrate large optomechanical coupling of a suspended carbon nanotube quantum dot and a microwave cavity, amplified by several orders of magnitude via the nonlinearity of Coulomb blockade. From an optomechanically induced transparency (OMIT) experiment, we obtain a single photon coupling of up to g0 = 2π ⋅ 95 Hz. This indicates that normal mode splitting and full optomechanical control of the carbon nanotube vibration in the quantum limit is reachable in the near future. Mechanical manipulation and characterization via the microwave field can be complemented by the manifold physics of quantum-confined single electron devices.

Interactions of solitary waves in integrable and nonintegrable lattices

We study how the dynamics of solitary wave (SW) interactions in integrable systems is different from that in nonintegrable systems in the context of crossing of two identical SWs in the (integrable) Toda and the (non-integrable) Hertz systems. We show that the collision process in the Toda system is perfectly symmetric about the collision point, whereas in the Hertz system, the collision process involves more complex dynamics. The symmetry in the Toda system forbids the formation of secondary SWs (SSWs), while the absence of symmetry in the Hertz system allows the generation of SSWs. We next show why the experimentally observed by-products of SW-SW interactions, the SSWs, must form in the Hertz system. We present quantitative estimations of the amount of energy that transfers from the SW after collision to the SSWs using (i) dynamical simulations, (ii) a phenomenological approach using energy and momentum conservation, and (iii) using an analytical solution introduced earlier to describe the SW in the Hertz system. We show that all three approaches lead to reliable estimations of the energy in the SSWs.

A coherent nanomechanical oscillator driven by single-electron tunnelling

A single-electron transistor embedded in a nanomechanical resonator represents an extreme limit of electron-phonon coupling. While it allows fast and sensitive electromechanical measurements, it also introduces backaction forces from electron tunnelling that randomly perturb the mechanical state. Despite the stochastic nature of this backaction, it has been predicted to create self-sustaining coherent mechanical oscillations under strong coupling conditions. Here, we verify this prediction using real-time measurements of a vibrating carbon nanotube transistor. This electromechanical oscillator has some similarities with a laser. The single-electron transistor pumped by an electrical bias acts as a gain medium and the resonator acts as a phonon cavity. Although the operating principle is unconventional because it does not involve stimulated emission, we confirm that the output is coherent. We demonstrate other analogues of laser behaviour, including injection locking, classical squeezing through anharmonicity, and frequency narrowing through feedback.

Mass Sensing for the Advanced Fabrication of Nanomechanical Resonators

We report on a nanomechanical engineering method to monitor matter growth in real time via e-beam electromechanical coupling. This method relies on the exceptional mass sensing capabilities of nanomechanical resonators. Focused electron beam-induced deposition (FEBID) is employed to selectively grow platinum particles at the free end of singly clamped nanotube cantilevers. The electron beam has two functions: it allows both to grow material on the nanotube and to track in real time the deposited mass by probing the noise-driven mechanical resonance of the nanotube. On the one hand, this detection method is highly effective as it can resolve mass deposition with a resolution in the zeptogram range; on the other hand, this method is simple to use and readily available to a wide range of potential users because it can be operated in existing commercial FEBID systems without making any modification. The presented method allows one to engineer hybrid nanomechanical resonators with precisely tailored functionalities. It also appears as a new tool for studying the growth dynamics of ultrathin nanostructures, opening new opportunities for investigating so far out-of-reach physics of FEBID and related methods.

Tunable doping of N and S in carbon nanotubes by retarding pyrolysis-gas diffusion to promote electrocatalytic hydrogen evolution

The doping amount of heteroatoms in N, S co-doped carbon nanotubes (CNT-NS) was accurately and extensively regulated by retarding pyrolysis-gas diffusion. The effect of the content of N and S on the hydrogen evolution activity of CNT-NS was revealed for the first time both experimentally and theoretically.