Nanomechanical resonators have been used to weigh cells, biomolecules and gas molecules, and to study basic phenomena in surface science, such as phase transitions and diffusion. These experiments all rely on the ability of nanomechanical mass sensors to resolve small masses. Here, we report mass sensing experiments with a resolution of 1.7 yg (1 yg = 10(-24) g), which corresponds to the mass of one proton. The resonator is a carbon nanotube of length ∼150 nm that vibrates at a frequency of almost 2 GHz. This unprecedented level of sensitivity allows us to detect adsorption events of naphthalene molecules (C(10)H(8)), and to measure the binding energy of a xenon atom on the nanotube surface. These ultrasensitive nanotube resonators could have applications in mass spectrometry, magnetometry and surface science.

* These authors contributed equally to this work. Damping is a key phenomenon in NEMS resonators. Not only does it impact the resonator dynamics (namely its motional amplitude and velocity), it also governs the performance of the resonator in various scientific and technological applications. These include studies of the quantum-to-classical transition [16] We perform measurements on graphene/nanotube resonators (Fig. 1a,b) at low temperature and in high vacuum, using a dilution refrigerator with a base temperature of 90 mK. The resonator is actuated electrostatically by applying an oscillating voltage AC V at frequency f between the resonator and a gate electrode (Fig. 1c). The motion is detected using the frequency-modulation (FM) mixing technique where the resonator To show that nonlinear damping in graphene and nanotube NEMSs is a robust phenomenon, we study three types of mechanical resonators: (i) nanotube under 3 tensile stress, (ii) nanotube with slack, and (iii) graphene sheet under tensile stress. We estimate the built-in stress in each of these devices by measuring their basic mechanical properties. As an example, Fig. 2a V for a nanotube resonator. The convex parabola has an electrostatic origin [21, 22] and indicates that the nanotube is under tensile stress (schematic diagram of Fig. 2a) [14,15]. The theory of damping finds its roots inWe arrive at the central result of the paper. Fig. 2b shows the resonant response of the stressed nanotube resonator for three different driving forces (these scale linearly with AC V ). As we increase the driving force, the resonance frequency shifts towards higher values and, simultaneously, the resonance peak broadens (see bars below the resonances). Both these effects are also displayed in Fig. 2c k is the Boltzmann constant, T the temperature, and e the electron charge). While the resonance shift is a known behavior (see below), the resonance broadening is a novel phenomenon. In larger resonators, the resonance width is indeed independent of the driving force (where m is the mass of the resonator).The same measurement is performed on the nanotube with slack (schematic of Fig. 2e) and on the graphene sheet under tensile stress (schematic of Fig. 3a). The resonance broadening is observed in all three types of resonators (Fig. 2c, Fig. 2e, Fig. 3a) and even at room temperature ( Supplementary Information, Fig. S10). This validates the robustness of the effect and confirms early optical measurements on graphene [12] showing similar behaviour. The resonance broadening does not stem from the coupling between electrons and mechanical vibrations [8,9] Supplementary Information, section J). The resonance shift shows different behaviors: It is significant for the resonators under tensile stress (Fig. 2d, Fig. 3b), yet it is negligible (Fig. 2f) and sometimes even negative ( Supplementary Information, Fig. S10) for nanotube resonators with slack. Further discussion, as well as additional electrical and mechanical characterizations, can be found in the Supplem...

A simple yet highly reproducible method to suppress contamination of graphene at low temperature inside the cryostat is presented. The method consists of applying a current of several mA through the graphene device, which is here typically a few $\mu$m wide. This ultra-high current density is shown to remove contamination adsorbed on the surface. This method is well suited for quantum electron transport studies of undoped graphene devices, and its utility is demonstrated here by measuring the anomalous quantum Hall effect.Comment: Accepted for publication in Applied Physics Letter

An important issue in nanoelectromechanical systems is developing small electrically driven motors. We report on an artificial nanofabricated motor in which one short carbon nanotube moves relative to another coaxial nanotube. A cargo is attached to an ablated outer wall of a multiwalled carbon nanotube that can rotate and/or translate along the inner nanotube. The motion is actuated by imposing a thermal gradient along the nanotube, which allows for subnanometer displacements, as opposed to an electromigration or random walk effect.

Since the advent of atomic force microscopy [1], mechanical resonators have been used to study a wide variety of phenomena, such as the dynamics of individual electron spins [2], persistent currents in normal metal rings [3], and the Casimir force [4,5].Key to these experiments is the ability to measure weak forces. Here, we report on force sensing experiments with a sensitivity of 12 zN/ √ Hz at a temperature of 1.2 K using a resonator made of a carbon nanotube. An ultra-sensitive method based on cross-correlated electrical noise measurements, in combination with parametric downconversion, is used to detect the low-amplitude vibrations of the nanotube induced by weak forces. The force sensitivity is quantified by applying a known capacitive force. A promising strategy for measuring lower forces is to employ resonators made of a molecular system, such as a carbon nanotube [14][15][16][17][18]. Nanotube resonators are characterized by an ultra-low mass M, which can be up to seven orders of magnitude lower than that of the ultra-soft cantilevers mentioned above [7], whereas their quality factor Q can be high [19] and their spring constant k 0 low. This has a great potential for generating an outstanding force sensitivity, whose classical limit is given byHere k B T is the thermal energy and γ the mechanical resistance [7]. This limit is set To efficiently convert weak forces into sizable displacements, we design nanotube resonators endowed with spring constants as low as ∼ 10 µN/m. This is achieved by fabri-2 cating the longest possible single-wall nanotube resonators. The fabrication process starts with the growth of nanotubes by chemical vapor deposition onto a doped silicon substrate coated with silicon oxide. Using atomic force microscopy (AFM), we select nanotubes that are straight over a distance of several micrometers, so that they do not touch the underlying substrate once they are released [21]. We use electron-beam lithography to pattern a source and a drain electrode that electrically contact and mechanically clamp the nanotube. We suspend the nanotube using hydrofluoric acid and a critical point dryer. Figure 1a shows a nanotube resonator that is 4 µm long. We characterize its resonant frequencies by driving it electrostatically and using a mixing detection method [18,22]. The lowest resonant frequency is 4.2 MHz (Fig. 1c). This gives a spring constant of 7 µN/m using an effective mass of 10 −20 kg, estimated from the size of the nanotube measured by AFM (supplementary information). This spring constant is comparable to that of the softest cantilevers fabricated so far [6]. When changing the gate voltage V DC g applied to the silicon substrate, the resonant frequency splits into two branches (Fig. 1c). These two branches correspond to the two fundamental modes; they vibrate in perpendicular directions (inset to Fig. 1c).We have developed an ultrasensitive detection method based on parametric downconversion, which (i) employs a cross-correlation measurement scheme to reduce the electrical noise ...