Vortex dynamics in Josephson junctions arrays

In this work we study the dynamics of vortices in two-dimensional overdamped Josephson Junctions Arrays (JJA) driven by dc current in a wide range of conditions varying magnetic field and temperature using experiments, numerical simulations and analytic studies.We develop the Fixed Phase method, a variation of numeric relaxation techniques in which we fix and control the phase of some islands, adjacent to the vortex center, while allowing all other phases in the system to relax.In this way we are able to pull and push the vortex uphill, as we are forcing the center of rotation of the vortex currents to be in a defined location, allowing us to calculate the potential energy of a vortex located in any arbitrary position.We use this method to study the potential energy of a vortex in a variety of situations in homogeneous and non-homogeneous JJA, such as arrays with defects, channel arrays and ratchets.We study the finite size effects in JJA by means of analytic and numerical tools.We implement the rings model, in which we replace the two-dimensional square array by a series of square, concentric, uncoupled rings. This is equivalent to disregarding the radial junctions that couple consecutive rings.In spite of its extreme simplicity, this model holds the main ingredients of the magnetic dependence of the energy.We combine this model with other terms that take into account the dependence in the position of the vortex to obtain a general expression for the potential energy of a vortex in a finite JJA with applied magnetic field.We also present an expression for the first critical field, corresponding to the value of the magnetic field in which the entrance of the first vortex becomes energetically favorable.We build and study JJA modulated to form periodic and asymmetrical potentials for the vortices, named ratchet potentials.The experimental results clearly show the existence of a rectification in the motion of vortices in these potentials.Under certain conditions we were able to observe a net movement in the direction opposite to the average driving force.We also identify for the first time the sign of the vortices being transported, whether they are vortices or antivortices.In addition our results show a strong interaction between collective effects (vortex-vortex interactions, structure of the vortex lattice) and the rectifying ratchet effect.We finally develop the anisotropic kinetic inductance technique, based on a novel kind of flat serpentine shaped coils.This technique shows clear advantages over traditional coils to measure two-dimensional samples such as JJA and superconducting films.The main difference is the very short distance separating coils and sample, all along the coils.We use this technique to study the dynamical regimes of vortices, when the force due to the current overcomes the pinning force and the vortices are pushed to motion.These regimes show an anisotropic character, attributed to the fact that the vortices in motion form a mobile structure with different coherence length in the directions parallel and perpendicular to movement