Towards magnetic force sensing of single molecules using suspended carbon nanotubes

Measuring the magnetic moment of a single spin remains an experimental challenge. Measuring such a moment at timescales relevant to relaxation in many small spin systems, even more so. However, such a measurement would permit detailed studies of the physics of these system and could probe new avenues of technology, such as real time use of single molecule magnets for quantum information processing. This thesis presents work towards realizing fast measurements of magnetic moments on the order of a single electron spin. This will be achieved by using a suspended carbon nanotube (CNT) resonator and a CNT-magnet coupling realized through nanoscale ferromagnets. Fabricating high quality CNT resonators for this application requires combining high quality, high throughput nanofabrication with carefully adapted growth of CNTs. The first part of this thesis describes fabrication steps developed to create full wafer arrays of CNT devices consisting of predefined contacts and fine local gates that will provide the fine magnetic structure that will allow strong CNT-magnet coupling. The growth of CNTs over these contacts is iterated to achieve long defect-free CNTs suspended over the trench between contacts. Low temperature measurements of one such device allow identification of potential fabrication improvements. The second section of this thesis describes simulations of the proposed sensing technique. Euler-Bernoulli beam models of the CNT allow extraction of resonant frequencies as a function of device parameters, and in particular allow us to identify the impact of a single Bohr magneton magnetic moment reversal. By mapping this frequency shift as a function of the device design and operating conditions we identify favourable device designs and optimal operating conditions to obtain maximum sensitivity. By comparing the achievable frequency shifts with intrinsic resonator noise, we calculate the fundamental signal to noise ratios of this sensing technique. By also considering transient response decay we extract optimal measurement bandwidths. These calculations reveal that magnetic switching on the order of a single Bohr magneton can be observed on timescales as short as 10us with this technique

Carbon nanotube electromechanical systems: Non-linear dynamics and self-oscillation

This thesis is motivated by the many sensing applications of carbon nanotube (CNT) nano-electromechanical systems (NEMS), both previous state-of-the-art demonstrations and proposed new uses. This research is particularly focused on the long term goal of realizing the magnetic force sensing of molecular nanomagnets, proposed in reference [1]. The fabrication of micron long, small diameter, high quality suspended carbon nanotubes is a challenging task. Integrating ferromagnetic structures which are incompatible with the CNT growth procedures increases this challenge. In this thesis, devices suitable for magnetic force sensing experiments are realized by separating the chemical vapour deposition growth of CNTs from the device contacts and gates, while maintaining CNT quality. Using conventional readout techniques, the low-temperature measurement of the CNT NEMS mechanical state is usually limited by the CNT contact resistance and capacitance of the measurement cabling/circuit. I describe the use of a heterojunction bipolar transistor (HBT) amplifying circuit operating at cryogenic temperatures near the device to measure the mechanical amplitude at microsecond timescales. A Coulomb rectification scheme, in which the probe signal is at much lower frequency than the mechanical drive signal, allows investigation of the transient response with strongly non-linear driving. The transient dynamics in both the linear and non-linear regimes are measured and modeled by including Duffing and non-linear damping terms in a harmonic oscillator equation. The non-linear regime can result in faster sensing response times, on the order of 10 μs for the device and circuit presented. Self-driven oscillations in suspended carbon nanotubes can create apparent instabilities in the electrical conductance of the CNT. In literature, such instabilities have been observed in kondo regime or high bias transport. In this thesis, I observed self-driven oscillations which created significant conduction within the nominally Coulomb-blockaded low-bias transport. Using a master equation system model, these oscillations are shown to be the result of strongly energy dependent electron tunneling to the contacts of high quality CNT NEMS operated at sub-Kelvin temperatures. Finally, in a separate research project, I consider the noise characterization of spin qubits interacting with the environment. In particular, I address the problem of probing the spectral density S(ω) of semi-classical phase noise using a spin interacting with a continuous-wave (CW) resonant excitation field. Previous CW noise spectroscopy protocols have been based on the generalized Bloch equations (GBE) or the filter function formalism, and assumed weak coupling to a Markovian bath. However, those protocols can substantially underestimate S(ω) at low frequencies when the CW pulse amplitude becomes comparable to S(ω). I derive the coherence decay more generally by extending to higher orders in the noise strength and discarding the Markov approximation. Numerical simulations show that this provides a more accurate description of the spin dynamics compared to a simple exponential decay, especially on short timescales. Exploiting these results, a new protocol is developed that uses an experiment at a single CW pulse amplitude to extend the spectral range over which S(ω) can be reliably determined, down to ω=0

Graphene nanogaps for the directed assembly of single-nanoparticle devices

Significant advances in the synthesis of low-dimensional materials with unique and tuneable electrical, optical and magnetic properties has led to an explosion of possibilities for realising hybrid nanomaterial devices with unconventional and desirable characteristics. However, the lack of ability to precisely integrate individual nanoparticles into devices at scale limits their technological application. Here, we report on a graphene nanogap based platform which employs the large electric fields generated around the point-like, atomically sharp nanogap electrodes to capture single nanoparticles from solution at predefined locations. We demonstrate how gold nanoparticles can be trapped and contacted to form single-electron transistors with a large coupling to a buried electrostatic gate. This platform offers a route to the creation of novel low-dimensional devices, nano- and optoelectronic applications, and the study of fundamental transport phenomena