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...

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 ...

Carbon nanotube mechanical resonators have attracted considerable interest because of their small mass, the high quality of their surface, and the pristine electronic states they host [1][2][3][4]. However, their small dimensions result in fragile vibrational states that are difficult to measure. Here we observe quality factors Q as high as 5×10 6 in ultra-clean nanotube resonators at a cryostat temperature of 30 mK, where we define Q as the ratio of the resonant frequency over the linewidth. Measuring such high quality factors requires both employing an ultra-low noise method to detect minuscule vibrations rapidly, and carefully reducing the noise of the electrostatic environment.We observe that the measured quality factors fluctuate because of fluctuations of the resonant frequency. The quality factors we measure are record high; they are comparable to the highest Q reported in mechanical resonators of much larger size [5, 6], a remarkable result considering that reducing the size of resonators is usually concomitant with decreasing quality factors. The combination of ultra-low size and very In recent years, endeavours to boost quality factors in nano and micromechanical resonators have been stimulated by the need to develop innovative approaches to sensing [7], signal processing [8] and quantum physics [9]. Strategies to enhance quality factors have proceeded along three main routes. Firstly, the quality of the host material has been improved. To this end, new materials have been employed, such as high tensile stress silicon nitride membranes [5, 10] and single crystal diamond films [11]. In addition, surface friction has been lowered by optimizing fabrication processes and reducing contamination [12].Secondly, schemes to isolate the resonator from its surrounding environment have been developed, based on new resonator layouts [13,14], and on optical trapping of thin membranes and levitated particles [15,16]. Thirdly, and most straightforwardly, Q-factors have been improved by operating resonators at cryogenic temperatures [17].Schemes to enhance Q-factors in nanotube resonators have focused on reducing contamination by growing ultra-clean nanotubes, and cooling resonators down to millikelvin temperatures [2]. Even though Q-factors, measured from the linewidth of driven resonances, have been improved up to ∼ 1.5 × 10 5 , they are still much lower than values routinely obtained with larger resonators fabricated from bulk materials using top-down techniques [6]. This result is somewhat disappointing, since the high crystallinity of nanotubes and their lack of dangling bonds at the surface are expected to minimize surface friction that limits the Q-factor in some nanomechanical systems [18].Here we find that the actual values of the Q-factors can be significantly higher than hitherto appreciated, but that revealing these values requires to perfect the measurement technique. Namely, the dynamics of the nanotube has to be captured in a regime of vanishingly small displacement in order to minimize nonline...