Adrian Bachtold

Science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems

We present the science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems, targeting an evolution in technology, that might lead to impacts and benefits reaching into most areas of society. This roadmap was developed within the framework of the European Graphene Flagship and outlines the main targets and research areas as best understood at the start of this ambitious project. We provide an overview of the key aspects of graphene and related materials (GRMs), ranging from fundamental research challenges to a variety of applications in a large number of sectors, highlighting the steps necessary to take GRMs from a state of raw potential to a point where they might revolutionize multiple industries. We also define an extensive list of acronyms in an effort to standardize the nomenclature in this emerging field.

Aharonov-Bohm oscillations in carbon nanotubes

When electrons pass through a cylindrical electrical conductor aligned in a magnetic field, their wave-like nature manifests itself as a periodic oscillation in the electrical resistance as a function of the enclosed magnetic flux. This phenomenon reflects the dependence of the phase of the electron wave on the magnetic field, known as the Aharonov–Bohm effect, which causes a phase difference, and hence interference, between partial waves encircling the conductor in opposite directions. Such oscillations have been observed in micrometre-sized thin-walled metallic cylinders and lithographically fabricated rings. Carbon nanotubes are composed of individual graphene sheets rolled into seamless hollow cylinders with diameters ranging from 1 nm to about 20 nm. They are able to act as conducting molecular wires, making them ideally suited for the investigation of quantum interference at the single-molecule level caused by the Aharonov–Bohm effect. Here we report magnetoresistance measurements on individual multi-walled nanotubes, which display pronounced resistance oscillations as a function of magnetic flux.We find that the oscillations are in good agreement with theoretical predictions for the Aharonov–Bohm effect in a hollow conductor with a diameter equal to that of the outermost shell of the nanotubes. In some nanotubes we also observe shorter-period oscillations, which might result from anisotropic electron currents caused by defects in the nanotube lattice.

Current-induced cleaning of graphene

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 milliamperes through the graphene device, which is here typically a few microns wide. This ultrahigh 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.

Nonlinear damping in mechanical resonators made from carbon nanotubes and graphene

The theory of damping is discussed in Newtons Principia and has been tested in objects as diverse as the Foucault pendulum, the mirrors in gravitational-wave detectors and submicrometre mechanical resonators. In general, the damping observed in these systems can be described by a linear damping force. Advances in nanofabrication mean that it is now possible to explore damping in systems with one or more atomic-scale dimensions. Here we study the damping of mechanical resonators based on carbon nanotubes and graphene sheets. The damping is found to strongly depend on the amplitude of motion, and can be described by a nonlinear rather than a linear damping force. We exploit the nonlinear nature of damping in these systems to improve the figures of merit for both nanotube and graphene resonators. For instance, we achieve a quality factor of 100,000 for a graphene resonator.The theory of damping finds its roots in Newton’s Principia [1] and has been exhaustively tested in objects as disparate as the Foucault pendulum, mirrors used in gravitational-wave detectors, and submicron mechanical resonators. Owing to recent advances in nanotechnology it is now possible to explore damping in systems with transverse dimensions on the atomic scale. Here, we study the damping of mechanical resonators based on a carbon nanotube [2-11] as well as on a graphene sheet [12-15], the ultimate one and two-dimensional nanoelectromechanical systems (NEMS). The damping is found to strongly depend on the amplitude of the motion; it is well described by a nonlinear force

Contacting carbon nanotubes selectively with low-ohmic contacts for four-probe electric measurements

Contact resistances of multiwalled nanotubes deposited on gold contact fingers are very large. We show that the contact resistances decrease by orders of magnitudes when the contact areas are selectively exposed to the electron beam in a scanning electron microscope. The focused electron beam enables the selection of one particular nanotube for electrical measurement in a four-terminal configuration, even if a loose network of nanotubes is deposited on the gold electrodes. For all measured nanotubes, resistance values lie in a narrow range of 0.35–2.6 kΩ at room temperature.

Ultrasensitive Mass Sensing with a Nanotube Electromechanical Resonator

Shrinking mechanical resonators to submicrometer dimensions (approximately 100 nm) has tremendously improved capabilities in sensing applications. In this Letter, we go further in size reduction using a 1 nm diameter carbon nanotube as a mechanical resonator for mass sensing. The performances, which are tested by measuring the mass of evaporated chromium atoms, are exceptional. The mass responsivity is measured to be 11 Hz x yg(-1) and the mass resolution is 25 zg at room temperature (1 yg = 10(-24) g and 1 zg = 10(-21) g). By cooling the nanotube down to 5 K in a cryostat, the signal for the detection of mechanical vibrations is improved and corresponds to a resolution of 1.4 zg.

Imaging mechanical vibrations in suspended graphene sheets.

We carried out measurements on nanoelectromechanical systems based on multilayer graphene sheets suspended over trenches in silicon oxide. The motion of the suspended sheets was electrostatically driven at resonance using applied radio frequency voltages. The mechanical vibrations were detected using a novel form of scanning probe microscopy, which allowed identification and spatial imaging of the shape of the mechanical eigenmodes. In as many as half the resonators measured, we observed a new class of exotic nanoscale vibration eigenmodes not predicted by the elastic beam theory, where the amplitude of vibration is maximum at the free edges. By modeling the suspended sheets with the finite element method, these edge eigenmodes are shown to be the result of nonuniform stress with remarkably large magnitudes (up to 1.5 GPa). This nonuniform stress, which arises from the way graphene is prepared by pressing or rubbing bulk graphite against another surface, should be taken into account in future studies on electronic and mechanical properties of graphene.

Subnanometer Motion of Cargoes Driven by Thermal Gradients Along Carbon Nanotubes

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.

Carbon Nanotube Based Bearing for Rotational Motions

We describe the fabrication of a nanoelectromechanical system consisting of a plate rotating around a multiwalled nanotube bearing. The nanotube has been engineered so that the sliding happens between different shells. The motion is possible thanks to the low static intershell friction, which we have estimated to be ∼0.85 MPa.

Coupling Mechanics to Charge Transport in Carbon Nanotube Mechanical Resonators

Tuning Carbon Nanotube Resonances Nanoscale resonators can be used in sensing and for processing mechanical signals. Single-walled carbon nanotubes have potential design advantages as resonators in that their oscillatory motion could be coupled to electron transport (see the Perspective by Hone and Deshpande). Steele et al. (p. 1103, published online 23 July) and Lassagne et al. (p. 1107, published online 23 July) report that the resonance frequency of a suspended single-walled carbon nanotube can be excited when operated as a single-electron transistor at low temperatures. Electrostatic forces are set up when the carbon nanotubes charge and discharge. The resonance frequency depends on applied voltages, and the coupling is strong enough to drive the mechanical motion into the nonlinear response regime. Differences in the responses of the devices in the two studies reflect in part the different quality factors of the resonators and different cryogenic temperatures. Individual electrons tunneling onto and out of a carbon nanotube can be used to tune its oscillatory motion. Nanoelectromechanical resonators have potential applications in sensing, cooling, and mechanical signal processing. An important parameter in these systems is the strength of coupling the resonator motion to charge transport through the device. We investigated the mechanical oscillations of a suspended single-walled carbon nanotube that also acts as a single-electron transistor. The coupling of the mechanical and the charge degrees of freedom is strikingly strong as well as widely tunable (the associated damping rate is ~3 × 106 Hz). In particular, the coupling is strong enough to drive the oscillations in the nonlinear regime.