The in-place growth of suspended carbon nanotubes facilitates the observation of both unperturbed electronic transport spectra and high-Q vibrational modes. For complex structures integrating, e.g., superconducting rf elements on-chip, selection of a chemically and physically resistant material that survives the chemical vapor deposition (CVD) process provides a challenge. We demonstrate the implementation of molybdenum-rhenium coplanar waveguide resonators that exhibit clear resonant behaviour at cryogenic temperatures even after having been exposed to nanotube growth conditions. The properties of the MoRe devices before and after CVD are compared to a reference niobium device.
We report the capacitive spring softening effect observed in single-walled carbon nanotube (SWNT) nanoelectromechanical (NEM) resonators. The nanotube resonators adopt dual-gate configuration with both bottom-gate and side-gate capable of tuning the resonance frequency through capacitive coupling. Interestingly, downward resonance frequency shifting is observed with increasing side-gate voltage, which can be attributed to the capacitive softening of spring constant. Furthermore, in-plane vibrational modes exhibit much stronger spring softening effect than out-of-plan modes. Our dual-gate desig…
We report on an electrical detection method of ultrasensitive carbon nanotube mechanical resonators. The noise floor of the detection method is reduced using a RLC resonator and an amplifier based on a high electron mobility transistor cooled at 4.2 K. This allows us to resolve the resonance frequency of nanotube resonators with an unprecedented quality. We show that the noise of the resonance frequency measured at 4.2 K is limited by the resonator itself, and not by the imprecision of the measurement. The Allan deviation reaches ~10^-5 at 125 ms integration time. When comparing the integratio…
We study electron mechanical coupling in a suspended carbon nanotube (CNT) quantum dot device. Electron spin couples to the flexural vibration mode due to spin-orbit coupling in the electron tunneling processes. In the weak coupling limit, i.e. electron-vibration coupling is much smaller than the electron energy scale, the damping and resonant frequency shift of the CNT resonator can be obtained by calculating the dynamical spin susceptibility. We find that strong spin-flip scattering processes in Kondo regime significantly affect the mechanical motion of the carbon nanotube: Kondo effect indu…
Mechanical resonators based on a single carbon nanotube are exceptional sensors of mass and force. The force sensitivity in these ultra-light resonators is often limited by the noise in the detection of the vibrations. Here, we report on an ultra-sensitive scheme based on a RLC resonator and a low-temperature amplifier to detect nanotube vibrations. We also show a new fabrication process of electromechanical nanotube resonators to reduce the separation between the suspended nanotube and the gate electrode down to $\sim 150$~nm. These advances in detection and fabrication allow us to reach $0.5…
The non-linear interaction between two mechanical resonances of the same freely suspended carbon nanotube resonator is studied. We find that in the Coulomb blockade regime, the non-linear 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 behavior. 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 nanotu…
Nanomechanical resonators are used with great success to couple mechanical motion to other degrees of freedom, such as photons, spins, and electrons. Mechanical vibrations can be efficiently cooled and amplified using photons, but not with other degrees of freedom. Here, we demonstrate a simple yet powerful method for cooling, amplification, and self-oscillation using electrons. This is achieved by applying a constant (DC) current of electrons through a suspended nanotube in a dilution fridge. We demonstrate cooling down to $4.6\pm 2.0$ quanta of vibrations. We also observe self-oscillation, w…
Bi-stable mechanical resonators play a significant role in various applications, such as sensors, memory elements, and quantum computing. While carbon nanotube (CNT) based resonators have been widely investigated as promising nano electro-mechanical devices, a bi-stable CNT resonator has never been demonstrated. Here, we report a new class of CNT resonators in which the nanotube is buckled upward. We show that a small upward buckling yields record electrical frequency tunability, whereas larger buckling can achieve Euler-Bernoulli (EB) bi-stability, the smallest mechanical resonator with two s…
We study the optical properties of MoS$_2$ nanotubes (NTs) with walls comprising dozens of monolayers. We reveal strong peaks in micro-photoluminescence ($μ$-PL) spectra when detecting the light polarized along the NT axis. We develop a model describing the optical properties of the nanotubes acting as optical resonators which support the quantization of whispering gallery modes inside the NT wall. The experimental observation of the resonances in $μ$-PL allows one to use them as a contactless method of the estimation of the wall width. Our findings open a way to use such NTs as polarization-s…
In this work, we present a detailed static and dynamic analysis of a recently reported electrically actuated buckled carbon nanotube (CNT) resonator, based on the Euler-Bernoulli beam theory. The system behavior is analyzed using the Galerkin reduced order model. We show that a simple single-modal analysis can already predict snap-through bi-stability in a buckled CNT resonator. However, we prove that the experimental data, in which the snap-through buckling occurs at a finite frequency, cannot be explained without taking into account out-of-plane motion. The buckled CNTs are the first type of…
With the objective of integrating single clean, as-grown carbon nanotubes into complex circuits, we have developed a technique to grow nanotubes directly on commercially available quartz tuning forks using a high temperature CVD process. Multiple straight and aligned nanotubes bridge the >100um gap between the two tips. The nanotubes are then lowered onto contact electrodes, electronically characterized in situ, and subsequently cut loose from the tuning fork using a high current. First quantum transport measurements of the resulting devices at cryogenic temperatures display Coulomb blockade c…
Helium is recognized as a model system for the study of phase transitions. Of particular interest is the superfluid phase in two dimensions. We report measurements on superfluid helium films adsorbed on the surface of a suspended carbon nanotube. We measure the mechanical vibrations of the nanotube to probe the adsorbed helium film. We demonstrate the formation of helium layers up to five atoms thickness. Upon increasing the vapour pressure, we observe layer-by-layer growth with discontinuities in both the number of adsorbed atoms and the speed of sound in the adsorbed film. These hitherto uno…
Bi-stable arched beams exhibiting Euler-Bernoulli snap-through buckling are vastly used as electronic devices in various applications, such as memory devices, energy harvesters, sensors, and actuators. Recently, we reported the realization of the smallest bi-stable resonator to date, in the form of a buckled suspended carbon nanotube (CNT), which exhibits a unique three-dimensional snap-through transition and an extremely large change in frequency as a result. In this article, we address a unique characteristic of these devices, in which a significant change in the DC conductance is also obser…
Synthesized micro- and nanotubes composed of transition metal dichalcogenides (TMDCs) such as MoS$_2$ are promising for many applications in nanophotonics, because they combine the abilities to emit strong exciton luminescence and to act as whispering gallery microcavities even at room temperature. In addition to tubes in the form of hollow cylinders, there is an insufficiently-studied class of twisted tubes, the flattened cross section of which rotates along the tube axis. As shown by theoretical analysis, in such nanotubes the interaction of electromagnetic waves excited at opposite sides of…
A magnetic field, through its vector potential, usually causes measurable changes in the electron wave function only in the direction transverse to the field. Here we demonstrate experimentally and theoretically that in carbon nanotube quantum dots, combining cylindrical topology and bipartite hexagonal lattice, a magnetic field along the nanotube axis impacts also the longitudinal profile of the electronic states. With the high (up to 17T) magnetic fields in our experiment the wave functions can be tuned all the way from "half-wave resonator" shape, with nodes at both ends, to "quarter-wave r…
We present a symmetry-adapted real-space formulation of Kohn-Sham density functional theory for cylindrical geometries and apply it to the study of large X (X=C, Si, Ge, Sn) nanotubes. Specifically, starting from the Kohn-Sham equations posed on all of space, we reduce the problem to the fundamental domain by incorporating cyclic and periodic symmetries present in the angular and axial directions of the cylinder, respectively. We develop a high-order finite-difference parallel implementation of this formulation, and verify its accuracy against established planewave and real-space codes. Using …
Hybrid circuit quantum electrodynamics (QED) involves the study of coherent quantum physics in solid state systems via their interactions with superconducting microwave circuits. Here we present an implementation of a hybrid superconducting qubit that employs a carbon nanotube as a Josephson junction. We realize the junction by contacting a carbon nanotube with a superconducting Pd/Al bi-layer, and implement voltage tunability of the qubit frequency using a local electrostatic gate. We demonstrate strong dispersive coupling to a coplanar waveguide resonator via observation of a resonator frequ…
We demonstrate sensitive and fast electrical measurements of a carbon nanotube mechanical resonator. The nanotube is configured as a single-electron transistor, whose conductance is a sensitive transducer for its own displacement. Using an impedance-matching circuit followed by a cryogenic amplifier, the vibrations can be monitored in real time. The sensitivity of this continuous displacement measurement approaches within a factor 470 of the standard quantum limit.
