B. Witkamp

Carbon Nanotubes as Ultrahigh Quality Factor Mechanical Resonators

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.

Strong Coupling Between Single-Electron Tunneling and Nanomechanical Motion

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. 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 105 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 motion.

Pumping of Vibrational Excitations in the Coulomb-Blockade Regime in a Suspended Carbon Nanotube

Low-temperature transport spectroscopy measurements on a suspended few-hole carbon nanotube quantum dot are presented, showing a gate-dependent harmonic excitation spectrum which, strikingly, occurs in the Coulomb-blockade regime. The quantized excitation energy corresponds to the scale expected for longitudinal vibrations of the nanotube. The electronic transport processes are identified as cotunnel-assisted sequential tunneling, resulting from nonequilibrium occupation of the mechanical mode. They appear only above a high-bias threshold at the scale of electronic nanotube excitations. We discuss models for the pumping process that explain the enhancement of the nonequilibrium occupation and show that it is connected to a subtle interplay between electronic and vibrational degrees of freedom.

Nanoelectromechanics of suspended carbon nanotubes

We discuss different types of measurements targetting the interplay of mechanical motion with electrical transport in suspended single-wall carbon nanotube devices. In driven resonator experiments, the transversal acoustical vibration mode is detected and identified at room temperature using ac down-mixing techniques. In contrast, low-temperature transport spectroscopy enables the observation of the longitudinal acoustic mode in the quantum limit in single electron tunnelling. This vibrational excitation can also be observed in higher order tunnelling current for appropriate electronic coupling to the leads. Experimental roads towards the quantum limit of the transversal vibration mode—as ultimate quantum-limited beam resonator—are explored, e.g. extending both abovementioned measurement techniques.

Spin-orbit interaction in chiral carbon nanotubes probed in pulsed magnetic fields

The magnetoconductance of an open carbon nanotube (CNT)-quantum wire was measured in pulsed magnetic fields. At low temperatures, we find a peculiar split magnetoconductance peak close to the chargeneutrality point. Our analysis of the data reveals that this splitting is intimately connected to the spin-orbit interaction and the tube chirality. Band-structure calculations suggest that the current in the peak regions is highly spin polarized, which calls for application in future CNT-based spintronic devices.

Self-detecting gate-tunable nanotube paddle resonators

We have fabricated suspended metal paddle resonators with carbon nanotubes functioning as self-detecting torsional springs. We observe gate-tunable resonances that either tune to higher or to lower frequencies when increasing the dc voltage on the back gate. We attribute the former modes to flexural vibrations of the paddle resonator, while the latter ones are identified as torsional vibrations. Compared to top-down silicon fabricated paddle resonators, nanotube springs have smaller torsional spring constants and provide a larger frequency tunability.

Single electron tunnelling through high-Q single-wall carbon nanotube NEMS resonators

By first lithographically fabricating contact electrodes and then as last step growing carbon nanotubes with chemical vapour deposition across the ready-made chip, many potential contamination mechanisms for nanotube devices can be avoided. Combining this with pre-defined trenches on the chip, such that the nanotubes are freely suspended above the substrate, enables the formation of highly regular electronic systems. We show that, in addition, such suspended ultra-clean nanotubes provide excellent high-frequency and low-dissipation mechanical resonators. The motion detection mechanism of our experiment is discussed, and we measure the effect of Coulomb blockade and the back-action of single electron tunneling on the mechanical motion. In addition data on the mechanical higher modes is presented.