H. B. Meerwaldt

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.

Large spin-orbit coupling in carbon nanotubes

It has recently been recognised that the strong spin-orbit interaction present in solids can lead to new phenomena, such as materials with non-trivial topological order. Although the atomic spin-orbit coupling in carbon is weak, the spin-orbit coupling in carbon nanotubes can be significant due to their curved surface. Previous works have reported spin-orbit couplings in reasonable agreement with theory, and this coupling strength has formed the basis of a large number of theoretical proposals. Here we report a spin-orbit coupling in three carbon nanotube devices that is an order of magnitude larger than previously measured. We find a zero-field spin splitting of up to 3.4 meV, corresponding to a built-in effective magnetic field of 29 T aligned along the nanotube axis. Although the origin of the large spin-orbit coupling is not explained by existing theories, its strength is promising for applications of the spin-orbit interaction in carbon nanotubes devices.

Strong and tunable mode coupling in carbon nanotube resonators

The nonlinear interaction between two mechanical resonances of the same freely suspended carbon nanotube resonator is studied. We find that, in the Coulomb-blockade regime, the nonlinear modal interaction is dominated by single-electron-tunneling processes and that the mode-coupling parameter can be tuned with the gate voltage, allowing both mode-softening and mode-stiffening behaviors. This is in striking contrast to tension-induced mode coupling in strings where the coupling parameter is positive and gives rise to a stiffening of the mode. The strength of the mode coupling in carbon nanotubes in the Coulomb-blockade regime is observed to be 6 orders of magnitude larger than the mechanical-mode coupling in micromechanical resonators.

Probing the charge of a quantum dot with a nanomechanical resonator

We have used the mechanical motion of a carbon nanotube (CNT) as a probe of the average charge on a quantum dot. Variations of the resonance frequency and the quality factor are determined by the change in average charge on the quantum dot during a mechanical oscillation. The average charge, in turn, is influenced by the gate voltage, the bias voltage, and the tunnel rates of the barriers to the leads. At bias voltages that exceed the broadening due to tunnel coupling, the resonance frequency and quality factor show a double dip as a function of gate voltage. We find that increasing the current flowing through the CNT at the Coulomb peak does not increase the damping, but in fact decreases damping. Using a model with energy-dependent tunnel rates, we obtain quantitative agreement between the experimental observations and the model. We theoretically compare different contributions to the single-electron induced nonlinearity, and show that only one term is significant for both the Duffing parameter and the mode coupling parameter. We also present additional measurements which support the model we develop: Tuning the tunnel barriers of the quantum dot to the leads gives a 200-fold decrease of the quality factor. Single-electron tunneling through an excited state of the CNT quantum dot also changes the average charge on the quantum dot, bringing about a decrease in the resonance frequency. In the Fabry-Perot regime, the absence of charge quantization results in a spring behavior without resonance frequency dips, which could be used, for example, to probe the transition from quantized to continuous charge with a nanomechanical resonator.

Observation of decoherence in a carbon nanotube mechanical resonator

In physical systems, decoherence can arise from both dissipative and dephasing processes. In mechanical resonators, the driven frequency response measures a combination of both, whereas time-domain techniques such as ringdown measurements can separate the two. Here we report the first observation of the mechanical ringdown of a carbon nanotube mechanical resonator. Comparing the mechanical quality factor obtained from frequency- and time-domain measurements, we find a spectral quality factor four times smaller than that measured in ringdown, demonstrating dephasing-induced decoherence of the nanomechanical motion. This decoherence is seen to arise at high driving amplitudes, pointing to a nonlinear dephasing mechanism. Our results highlight the importance of time-domain techniques for understanding dissipation in nanomechanical resonators, and the relevance of decoherence mechanisms in nanotube mechanics.

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.

Submicrosecond-timescale readout of carbon nanotube mechanical motion

We report fast readout of the motion of a carbon nanotube mechanical resonator. A close-proximity high electron mobility transistor amplifier is used to increase the bandwidth of the measurement of nanotube displacements from the kHz to the MHz regime. Using an electrical detection scheme with the nanotube acting as a mixer, we detect the amplitude of its mechanical motion at room temperature with an intermediate frequency of 6 MHz and a timeconstant of 780 ns, both up to five orders of magnitude faster than achieved before. The transient response of the mechanical motion indicates a ring-down time faster than our enhanced time resolution, placing an upper bound on the contribution of energy relaxation processes to the room temperature mechanical quality factor.