Diffusion-induced dissipation and mode coupling in nanomechanical resonators

We study a system consisting of a particle adsorbed on a carbon nanotube resonator. The particle is allowed to diffuse along the resonator, in order to enable study of e.g. room temperature mass sensing devices. The system is initialized in a state where only the fundamental vibration mode is excited, and the ring-down of the system is studied by numerically and analytically solving the stochastic equations of motion. We find two mechanisms of dissipation, induced by the diffusing adsorbate. First, short-time correlations between particle and resonator motions means that the net effect of the former on the latter does not average out, but instead causes dissipation of vibrational energy. For vibrational amplitudes that are much larger than the thermal energy this dissipation is linear; for small amplitudes the decay takes the same form as that of a nonlinearly damped oscillator. Second, the particle diffusion mediates a coupling between vibration modes, enabling energy transfer from the fundamental mode to excited modes, which rapidly reach thermal equilibrium.Comment: 8 pages, 7 figure

Numerical Studies of Vortex Core States in Type II Superconductors

In this thesis, we study an isolated vortex in an s-wave superconductor by solving the Bogoliubov-de Gennes equations self-consistently on a disc. We calculate the order parameter and supercurrent profiles, as well as the distribution of quasiparticle states. In contrast to quasi-classical treatments, the ratio Δ∞/EF between the order parameter and the Fermi energy is not assumed negligible. We study a regime where this ratio is on the order of 10-1, relevant to high-temperature superconductors. In this regime, we find a Friedel-like oscillation in the order parameter profile at low temperatures. This oscillation is attributed to an increased level spacing of the quasiparticle states, causing a decrease of the number of states present inside the superconducting energy gap. The results are in good agreement with previously published works. In future studies, the method used in this thesis will be generalized to d-wave superconductors.I detta examensarbete studeras en ensam virvel i en s-vågssupraledare genom att självkonsistent lösa Bogoliubov och de Gennes' ekvationer på en cylinderskiva. Vi beräknar ordningsparameter- och superströmsprofiler, samt fördelningen av kvasipartikeltillstånd. Till skillnad från i kvasiklassiska metoder så antas inte kvoten Δ∞/EF mellan ordningsparametern och Fermi-energin vara negligerbar. Vi studerar en regim där denna kvot är av storleksordningen 10-1, vilket är fallet i högtemperatur-supraledare. Vid låga temperaturer finner vi i denna regim en Friedelliknande oscillation i ordningsparameterprofilen. Denna oscillations förklaras genom att separationen mellan kvasipartikeltillstånd ökar, vilket får som effekt att färre tillstånd ryms innanför det supraledande energigapet. Våra resultat överensstämmer väl med tidigare publicerade artikler. I framtida studier kommer metoden vi använder i detta examensarbete att generaliseras till d-vågssupraledare

Diffusion-Induced Nonlinear Dynamics in Carbon Nanomechanical Resonators

The emergence of nanoelectromechanical systems has enabled the development of sensors capable of detecting mass, charge, force, position, and spin with an unprecedented precision. In particular, the low mass, high resonant frequency, and high quality factor of carbon nanomechanical resonators make them ideal for the creation of a high sensitivity mass sensor. Carbon nanotube resonators are indeed the basis of the most sensitive mass sensors to date, whereas resonators made from suspended graphene monolayers are potentially capable of a very high rate of operation, due to their large surface area. A complicating factor is that the available mass measurement schemes rely on that the measured mass remains stationary, something that is no longer true at non-cryogenic temperatures. In this thesis, the effect of an elevated ambient temperature on a mass-resonator system is studied by simulating ring-down experiments. Thermal fluctuations in the position of the mass on the resonator introduce a stochastic force in the system equations of motion; these stochastic differential equations are here solved analytically and numerically. The unperturbed resonator is modeled as an undamped linear oscillator, but the addition of a diffusing mass induces nonlinear dynamics in the system. The presence of the particle mediates a coupling between vibrational modes, that acts as a new dissipation channel. Additionally, short-time correlations between the motion of the diffusing particle and the vibrating resonator results in a second dissipation mechanism, that causes a nonexponential decay of the vibrational energy. For vibrational amplitudes that are much larger than the thermal energy this dissipation is linear; for small amplitudes the decay takes the same form as that of a nonlinearly damped oscillator

Diffusion-Induced Nonlinear Dynamics in Carbon Nanomechanical Resonators

The emergence of nanoelectromechanical systems has enabled the development of sensors capable of detecting mass, charge, force, position, and spin with an unprecedented precision. In particular, the low mass, high resonant frequency, and high quality factor of carbon nanomechanical resonators make them ideal for the creation of a high sensitivity mass sensor. Carbon nanotube resonators are indeed the basis of the most sensitive mass sensors to date, whereas resonators made from suspended graphene monolayers are potentially capable of a very high rate of operation, due to their large surface area. A complicating factor is that the available mass measurement schemes rely on that the measured mass remains stationary, something that is no longer true at non-cryogenic temperatures. In this thesis, the effect of an elevated ambient temperature on a mass-resonator system is studied by simulating ring-down experiments. Thermal fluctuations in the position of the mass on the resonator introduce a stochastic force in the system equations of motion; these stochastic differential equations are here solved analytically and numerically. The unperturbed resonator is modeled as an undamped linear oscillator, but the addition of a diffusing mass induces nonlinear dynamics in the system. The presence of the particle mediates a coupling between vibrational modes, that acts as a new dissipation channel. Additionally, short-time correlations between the motion of the diffusing particle and the vibrating resonator results in a second dissipation mechanism, that causes a nonexponential decay of the vibrational energy. For vibrational amplitudes that are much larger than the thermal energy this dissipation is linear; for small amplitudes the decay takes the same form as that of a nonlinearly damped oscillator