We study the elastic deformation of few layers (5 to 25) thick freely suspended MoS 2 nanosheets by means of a nanoscopic version of a bending test experiment, carried out with the tip of an atomic force microscope. The Young's modulus of these nanosheets is extremely high (E = 0.33 TPa), comparable to that of graphene oxide, and the deflections are reversible up to tens of nanometers. This is the pre-peer reviewed version of the following article: A.Castellanos-Gomez et al. "Elastic properties of freely suspended MoS 2 nanosheets".

Nanoscale resonators that oscillate at high frequencies are useful in many measurement applications.We studied a high-quality mechanical resonator made from a suspended carbon nanotube driven into motion by applying a periodic radio frequency potential using a nearby antenna. Single-electron charge fluctuations created periodic modulations of the mechanical resonance frequency. A quality factor exceeding 10 5 allows the detection of a shift in resonance frequency caused by the addition of a single-electron charge on the nanotube. Additional evidence for the strong coupling of mechanical motion and electron tunneling is provided by an energy transfer to the electrons causing mechanical damping and unusual nonlinear behavior. We also discovered that a direct current through the nanotube spontaneously drives the mechanical resonator, exerting a force that is coherent with the high-frequency resonant mechanical The combination of a high resonance frequency and a small mass also makes nanomechanical resonators attractive for a fundamental study of mechanical motion in the quantum limit [6, 7, 8, 9]. For a successful observation of quantum motion of a macroscopic object, a high-frequency nanoscale resonator must have low dissipation (which implies a high quality-factor Q), and a sensitive detector with minimum back-action (i.e. quantum limited) [10, 11]. Here, we demonstrate a dramatic backaction that strongly couples a quantum dot detector to the resonator dynamics of a carbon nanotube, and which, in the limit of strong feedback, spontaneously excites large amplitude resonant mechanical motion.Nanomechanical resonators have been realized by etching down larger structures. In small devices, however, surfaces effects impose a limit on the quality-factor [2]. Alternatively, suspended carbon nanotubes can be used to avoid surface damage from the (etching) fabrication process. We recently developed a mechanical resonator based on an ultra-clean carbon nanotube with high resonance frequencies of several 100 MHz and a Q exceeding 10 5 [12]. Here, we exploit this resonator to explore a strong coupling regime between single electron tunneling and nanomechanical motion. We followed the pioneering approaches in which aluminium single electron transistors were used as position detectors [6, 7, 8] and AFM cantilevers as resonators [13,14,15]; however, our experiment is in the limit of much stronger electro-mechanical coupling, achieved by embedding a quantum dot detector in the nanomechanical resonator itself.Our device consists of a nanotube suspended across a trench that makes electrical contact to two metal electrodes ( Fig. 1). Electrons are confined in the nanotube by Schottky barriers at the Pt metal contacts, forming a quantum dot in the suspended segment. The nanotube growth is the last step in the fabrication process, yielding ultra-clean devices [16], as demonstrated by the four-fold shell-filling of the Coulomb peaks (Fig. 1C). All measurements were performed at a temperature of 20 mK with an electron temperat...

Mechanical systems are ideal candidates for studying quantum behavior of macroscopic objects. To this end, a mechanical resonator has to be cooled to its ground state and its position has to be measured with great accuracy. Currently, various routes to reach these goals are being explored. In this review, we discuss different techniques for sensitive position detection and we give an overview of the cooling techniques that are being employed. The latter include sideband cooling and active feedback cooling. The basic concepts that are important when measuring on mechanical systems with high accuracy and/or at very low temperatures, such as thermal and quantum noise, linear response theory, and backaction, are explained. From this, the quantum limit on linear position detection is obtained and the sensitivities that have been achieved in recent opto and nanoelectromechanical experiments are compared to this limit. The mechanical resonators that are used in the experiments range from meter-sized gravitational wave detectors to nanomechanical systems that can only be read out using mesoscopic devices such as single-electron transistors or superconducting quantum interference devices. A special class of nanomechanical systems are bottom-up fabricated carbon-based devices, which have very high frequencies and yet a large zero-point motion, making them ideal for reaching the quantum regime. The mechanics of some of the different mechanical systems at the nanoscale is studied. We conclude this review with an outlook of how state-of-the-art mechanical resonators can be improved to study quantum mechanics

We have observed the transversal vibration mode of suspended carbon nanotubes at millikelvin temperatures by measuring the single-electron tunneling current. The suspended nanotubes are actuated contact-free by the radio frequency electric field of a nearby antenna; the mechanical resonance is detected in the time-averaged current through the nanotube. Sharp, gate-tunable resonances due to the bending mode of the nanotube are observed, combining resonance frequencies of up to nu(0) = 350 MHz with quality factors above Q = 10(5), much higher than previously reported results on suspended carbon nanotube resonators. The measured magnitude and temperature dependence of the Q factor shows a remarkable agreement with the intrinsic damping predicted for a suspended carbon nanotube. By adjusting the radio frequency power on the antenna, we find that the nanotube resonator can easily be driven into the nonlinear regime.

A theoretical and experimental investigation is presented on the intermodal coupling between the flexural vibration modes of a single clamped-clamped beam. Nonlinear coupling allows an arbitrary flexural mode to be used as a self-detector for the amplitude of another mode, presenting a method to measure the energy stored in a specific resonance mode. Experimentally observed complex nonlinear dynamics of the coupled modes are quantitatively captured by a model which couples the modes via the beam extension; the same mechanism is responsible for the well-known Duffing nonlinearity in clamped-clamped beams.PACS numbers: 85.85.+j, 05.45.-a An important topic in nanomechanics is the motion detection of mechanical resonators. Several schemes have been proposed to attain sensitivities near the quantum limit of mechanical motion [1], whereas applicationdriven research is focussed on on-chip detection [2] and readout of resonator arrays [3]. Central in any detection scheme is the coupling of a mechanical resonator to another system, which transduces the motion into a measurable quantity. Examples of sensitive detectors include a single-electron transistor [4], a microwave cavity [5], or an optical interferometer [6]. A second mechanical resonator can also be used to detect the motion of the resonator [7,8]. Such a system of coupled resonators has been proposed as a quantum nondemolition detection scheme, in which one resonator is in a quantum state [9]. Coupling between different mechanical resonators is often present in large-scale integrated arrays due to electrostatic [7] and mechanical interaction [8]. Coupling between individual resonators can also lead to complex behavior, which is theoretically well-documented [10].In this Letter, we study the coupling between vibrational modes in a single beam resonator. We demonstrate that flexural modes are coupled by the displacementinduced tension in the beam. Using this coupling, the displacement of any mode can be detected by measuring the response of another mode, making otherwise undetectable modes visible. We present a general theoretical framework based on the Euler-Bernoulli equation extended with displacement-induced tension. The model quantitatively describes the complex dynamic behavior observed in the regime where two modes are simultaneously driven nonlinear. The coupling mechanism plays an prominent role in the dynamics of carbon nanotube resonators and resonators under high tension, and should be taken into account when describing such systems accurately.Experiments are performed on a single-crystalline silicon beam with dimensions L × w × h = 1000 × 35×6 µm 3 fabricated by patterning a silicon-on-insulator wafer and subsequent wet etching. The resonator is placed in a magnetic field of B = 2.1 T and a magnetomotive technique [3,11] is used to detect the mechanical motion of the beam at room temperature and atmospheric pressure (see Figure 1a). The beam is driven at multiple frequencies by sending alternating currents through a conductive aluminum path, evapo...

We have measured the mechanical properties of few-layer graphene and graphite flakes that are suspended over circular holes. The spatial profile of the flake's spring constant is measured with an atomic force microscope. The bending rigidity of and the tension in the membranes are extracted by fitting a continuum model to the data. For flakes down to eight graphene layers, both parameters show a strong thickness dependence. We predict fundamental resonance frequencies of these nanodrums in the gigahertz range based on the measured bending rigidity and tension.

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Classical and quantum dynamics of nanomechanical systems promise new applications in nanotechnology 18,19 and fundamental tests of quantum mechanics in mesoscopic objects 2,9 . Recent development of nanoscale electromechanical (NEMS) and optomechanical systems has enabled cooling of mechanical systems to their quantum ground state 7,8 , which brings the possibility of quantum information processing with mechanical devices 20,21 . On the other hand, for practical application at room temperature -such as signal processing 22 A rendering of the optomechanical system used in this study is shown in Fig. 1a. ) and yet to allow large oscillation amplitudes. Due to the residual compressive stress introduced by the SOI wafer bonding process, the freestanding doubly clamped beams are slightly buckled and have two stable configurations at rest 37 : buckled up and buckled down (see Fig. 1b). Therefore, the out-of-plane motion of the buckled beam can be described by a double-well potential, where both the 'up'and 'down' states correspond to the minima in the potential. The thermomechanical displacement noise spectra in Fig. 1e show that the two states have slightly different mechanical resonance frequencies, which indicates that the double-well potential is not completely symmetric.The two mechanical states are discriminated in optical transmission measurements because the optical mode has a different effective refractive index in the two states:when the waveguide is closer to the substrate (buckled-down state) the effective refractive index is larger than in the buckled-up state as the optical mode interacts stronger with the substrate. Therefore the optical cavity resonance shifts towards longer wavelengths when the resonator flips from the buckled-up state to the buckled-down state. Consequently, the optical cavity has distinct optical resonances in the two stable configurations as shown in low power optical transmission spectra in Fig. 1c. The low 4 power spectrum probes the static optomechanical resonances, but at high power the mechanical resonator starts to oscillate when the pump wavelength is scanned close to the optical resonance. Fig. 1d shows the optical transmission spectrum measured when the input optical power is well above the threshold for self-sustained oscillations (SSO) of ~600 μW. When the wavelength is scanned across the optical resonance, the transmission no longer shows the low-power Lorentzian shape, rather the resonance is dragged from the "up" to the "down" state: as soon the laser is blue detuned w.r.t. the "up" state, the self-sustained oscillations start and the cavity frequency oscillates back and forth with an amplitude A p-p ·g, where A p-p is the mechanical resonator oscillation amplitude. The SSO in turn modulate the optical transmission at the mechanical oscillation frequency, indicated by the high-frequency components of the optical transmission ( Fig. 1d). The SSO appear in the entire wavelength range between the "up"and "down" state optical modes, which indicates that the energy of th...