Quantum Phase Transitions and Vortex Dynamics in Superconducting Networks

Josephson junction arrays are ideal model systems where a variety of phenomena, phase transitions, frustration effects, vortex dynamics, chaos, to mention a few of them, can be studied in a controlled way. In this review we focus on the quantum dynamical properties of low capacitance Josephson junction arrays. The two characteristic energy scales in these systems are the Josephson energy, associated to the tunneling of Cooper pairs between neighboring islands, and the charging energy, which is the energy cost to add an extra electron charge to a neutral island. The phenomena described in this review stem from the competition between single electron effects with the Josephson effect. One example is the (quantum) Superconductor-Insulator phase transition which occurs by varying the ratio between the coupling constants and/or by means of external magnetic/electric fields. We will describe how the phase diagram depends on the various control paramters and the transport properties close to the quantum critical point. The relevant topological excitations on the superconducting side of the phase diagram are vortices. In low capacitance junction arrays vortices behave as massive underdamped particles that can exhibit quantum behaviour. We will report on the various experiments and theoretical treatments on quantum vortex dynamics.Comment: To be published in Physics Reports. Better quality figures can be obtained upon reques

Efficient readout of micromechanical resonator arrays in ambient conditions

We present a method for efficient spectral readout of mechanical resonator arrays in dissipative environments. Magnetomotive drive and detection is used to drive double clamped resonators in the nonlinear regime. Resonators with almost identical resonance frequencies can be tracked individually by sweeping the drive power. Measurements are performed at room temperature and atmospheric pressure. These conditions enable application in high throughput resonant sensor arrays.Comment: 4 pages, 4 figure

On Mean-Field Theory of Quantum Phase Transition in Granular Superconductors

In previous work on quantum phase transition in granular superconductors, where mean-field theory was used, an assumption was made that the order parameter as a function of the mean field is a convex up function. Though this is not always the case in phase transitions, this assumption must be verified, what is done in this article

Superconducting to normal state phase boundary in arrays of ultrasmall Josephson junctions

We study the competition between Josephson and charging energies in two-dimensional arrays of ultrasmall Josephson junctions, when the mutual capacitance is dominant over the self-capacitance. Our calculations involve a combination of an analytic WKB renormalization group approach plus nonperturbative Quantum Monte Carlo simulations. We consider the zero frustration case in detail and we are able to make a successful comparison between our results and those obtained experimentally.Comment: 14 pages + 2 postscript figures, REVTEX. THU-9412

Strongly coupled modes in a weakly driven micromechanical resonator

We demonstrate strong coupling between the flexural vibration modes of a clamped-clamped micromechanical resonator vibrating at low amplitudes. This coupling enables the direct measurement of the frequency response via amplitude- and phase modulation schemes using the fundamental mode as a mechanical detector. In the linear regime, a frequency shift of $\mathrm{0.8\,Hz}$ is observed for a mode with a line width of $\mathrm{5.8\,Hz}$ in vacuum. The measured response is well-described by the analytical model based on the Euler-Bernoulli beam including tension. Calculations predict an upper limit for the room-temperature Q-factor of $\mathrm{4.5\times10^5}$ for our top-down fabricated micromechanical beam resonators.Comment: 9 pages, 2 figure

Nonlinear Viscous Vortex Motion in Two-Dimensional Josephson-Junction Arrays

When a vortex in a two-dimensional Josephson junction array is driven by a constant external current it may move as a particle in a viscous medium. Here we study the nature of this viscous motion. We model the junctions in a square array as resistively and capacitively shunted Josephson junctions and carry out numerical calculations of the current-voltage characteristics. We find that the current-voltage characteristics in the damped regime are well described by a model with a {\bf nonlinear} viscous force of the form $F_D=\eta(\dot y)\dot y={{A}\over {1+B\dot y}}\dot y$, where $\dot y$ is the vortex velocity, $\eta(\dot y)$ is the velocity dependent viscosity and $A$ and $B$ are constants for a fixed value of the Stewart-McCumber parameter. This result is found to apply also for triangular lattices in the overdamped regime. Further qualitative understanding of the nature of the nonlinear friction on the vortex motion is obtained from a graphic analysis of the microscopic vortex dynamics in the array. The consequences of having this type of nonlinear friction law are discussed and compared to previous theoretical and experimental studies.Comment: 14 pages RevTex, 9 Postscript figure

Nanomechanical properties of few-layer graphene membranes

We have measured the mechanical properties of few-layer graphene and graphite flakes that are suspended over circular holes. The spatial profile of the flake's spring constant is measured with an atomic force microscope. The bending rigidity of and the tension in the membranes are extracted by fitting a continuum model to the data. For flakes down to eight graphene layers, both parameters show a strong thickness-dependence. We predict fundamental resonance frequencies of these nanodrums in the GHz range based on the measured bending rigidity and tension.Comment: 9 pages, 3 figures, This article has been accepted by Appl. Phys. Lett. After it is published, it will be found at http://apl.aip.org