It has recently been recognized 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 coupli
ng 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 measured before. 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. While 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.
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 potent
ial using a nearby antenna. Single-electron charge fluctuations created periodic modulations of the mechanical resonance frequency. A quality factor exceeding 10^5 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.
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-tuneable resonances due to the bending mode of the nanotube are observed, combining resonance frequencies of up to u_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 RF power on the antenna, we find that the nanotube resonator can easily be driven into the non-linear regime.
Quantum dots defined in carbon nanotubes are a platform for both basic scientific studies and research into new device applications. In particular, they have unique properties that make them attractive for studying the coherent properties of single e
lectron spins. To perform such experiments it is necessary to confine a single electron in a quantum dot with highly tunable barriers, but disorder has until now prevented tunable nanotube-based quantum-dot devices from reaching the single-electron regime. Here, we use local gate voltages applied to an ultra-clean suspended nanotube to confine a single electron in both a single quantum dot and, for the first time, in a tunable double quantum dot. This tunability is limited by a novel type of tunnelling that is analogous to that in the Klein paradox of relativistic quantum mechanics.
