Torsional electromechanical quantum oscillations in carbon nanotubes.

Carbon nanotubes can be distinctly metallic or semiconducting depending on their diameter and chirality. Here we show that continuously varying the chirality by mechanical torsion can induce conductance oscillations, which can be attributed to metal –semiconductor periodic transitions. The phenomenon is observed in multiwalled carbon nanotubes, where both the torque and the current are shown to be carried predominantly by the outermost wall. The oscillation period with torsion is consistent with the theoretical shifting8 of the corners of the first Brillouin zone of graphene across different subbands allowed in the nanotube. Beyond a critical torsion, the conductance irreversibly drops due to torsional failure, allowing us to determine the torsional strength of carbon nanotubes. Carbon nanotubes could be ideal torsional springs for nanoscopic pendulums, because electromechanical detection of motion could replace the microscopic detection techniques used at present. Our experiments indicate that carbon nanotubes could be used as electronic sensors of torsional motion in nanoelectro-mechanical systems11. Owing to the promise of carbon nanotubes for application in nanoelectromechanical systems (NEMS), the effects of mechanical deformations on their electronic properties have attracted great interest. Linear electromechanical responses have been observed for axial15,16, radial17 and flexural18 strain. Torsional electromechanical effects have been predicted by several groups, but not yet observed. Conductance oscillations have been observed with magnetic fields and gating21,22, but not with strain. To measure the conductance of carbon nanotubes under varying torsional strain, we built torsional nanotube-based NEMS as shown in Fig. 1, where a suspended multiwalled carbon nanotube is mechanically and electrically connected to a pair of electrodes and a small pedal in the middle. The nanotube is twisted by pressing against the pedal with an atomic force microscope (AFM) tip, and the electrodes allow us to simultaneously measure the twoterminal conductance across the nanotube. The devices were fabricated in an electron-beam lithography lift-off process, followed by wet etching and critical-point drying. Similar devices have been built with multiwalled and single-wall carbon nanotubes, and used as torsional pendulums and nanorotors, but no torsion-dependent electrical measurements were reported. Before the torsional electromechanical measurements, we characterized independently the torsional mechanical properties and the electronic properties of several nanotube devices. The former were studied by measuring force versus pedal-deflection curves at different points along the long axis of the pedal (Fig. 2a). The results agree with Archimedes’ law of the lever (Fig. 2b), indicating that the pedal compliance is mostly due to nanotube torsion, rather than to bending or stretching. The corresponding torsional spring constants (see Supplementary Information for full data table) corresponded to the shear moduli that are expected for hollow cylinders, rather than for solid rods, indicating that torsion involves predominantly the outermost wall, in accordance with previous reports (inner walls were reported to be involved after a much larger number of actuations than were performed here). The elasticity of the torsion is evident both from the reversible and linear response to the force applied by the AFM tip, and from the reversible pedal deflection due to charging under a scanning electron microscope (see Supplementary Information, movie). The differential conductance as a function of bias in relaxed devices exhibits typical hyperbolic shapes (Fig. 2c), similar to those observed in pristine arc-grown multiwalled carbon nanotubes, where conduction is ballistic across the outermost wall, increasing with bias as more channels become accessible. The low-bias differential conductance is smaller than the quantum conductance owing to the large contact resistance. From this preliminary characterization we conclude that both the torque and the current are predominantly carried by the outermost wall. Hence, our multiwalled nanotubes effectively act as large-diameter single-wall nanotubes, where the inner walls provide an inert mechanical support against bending and collapse. The torsional electromechanical response of the carbon nanotubes was studied by repeatedly pressing and retracting an AFM tip on one point of the pedal (about halfway between the nanotube and the pedal edge), while monitoring the lowbias differential conductance using a lock-in amplifier. The applied a.c. bias amplitude (10 mV) was smaller than the nanotube bandgap ( 30 meV), and the a.c. frequency (1 kHz) was significantly higher than the acquisition rate (loop rate, 0.2 Hz; 512 measurements per loop). The AFM probe was driven at resonance ( 70 kHz), with a sensing amplitude (60–80 nm) to detect its landing and detachment from the pedal by following LETTERS