PhD project opportunity: Emergence of static and dynamic configurations of vortices in type 1.5 superconductors
Figure 0 Overview of figures show below. Introduction The standard classification of superconductors divides them into two classes according to their behavior in the presence of an external magnetic field: Type-I superconductors expel low magnetic fields completely (the so-called Meissner state), while elevated fields produce macroscopic normal domains in the interior of the superconductor. Type-II superconductors possess stable vortex excitations which can form a vortex lattice as the energetically preferred state in an applied magnetic field. In the study of type-II superconductors, the vortices are often described as (point-like) particles that repel each other. As the particles can form a hexagonal lattice (i.e. a solid), or -- if exposed to a high temperature -- melt into a liquid, this system is referred to as 'vortex matter'. In studies of vortex matter in thin films, one investigates repelling particles in a two-dimensional universe. As material imperfections create areas in the superconductor that attract the particles, and any supercurrents flowing through the sample will drive the vortices in a particular direction, there is very rich physics in these systems with a variety of emerging vortex matter configurations. For example, in the presence of strong disorder, vortices flow across the sample in an avalanche like fashion, where as for weaker disorder they form a (nearly) hexagonal moving lattice (technically known now as a moving Bragg glass). More recently, it has been predicted (2005) and later confirmed experimentally (2009) that in particular materials there can be stable vortices with intervortex interaction which is attractive at longer range and repulsive at short range (in contrast to purely repulsive interaction between vortices in single-component superconductors). See also this summary. The existence of a long-range interaction that is repulsive and attractive (for different particle spacings) opens up a significantly wider range of options for static stable configurations (see figure 2 below), and promises very rich dynamic behaviour. Project outline In this project, we will study the statics and dynamics of vortex matter in superconductors of type 1.5, in particular to understand the number of mesophases shown in figure 2, and to extend the studies to the dynamics of these systems when driven by a driving force. By introducing a pinning potential and varying the sample geometry, the dynamics of the particles can be modified controlled. These systems can be realised experimentally, and predicted simulation results confirmed (or experimental results understood using the simulations). While this research is fairly fundamental, it may pave the way to new data processing techniques, or -- in the shorter term -- improve the performance of superconducting wires in applications such as Magnetic Resonance Imaging (MRI), or current transport over long distances. Methodology Numerical simulations of these multi-particle system use Metropolis Monte Carlo and (Langevin) Molecular Dynamics methods. We use Python combined with C/C++/OpenCL/CUDA code where necessary. The group has experience in these simulations from extensive studies of vortex matter dynamics in type 2 superconductors, and the development and use of the vdsim simulation code. Funding This project can be funded through the Doctoral Training Centre in Complex Systems Simulations (see http://www.icss.soton.ac.uk). 
Figure 1 A hexagonal array of purely repulsive vortices (represented as red spheres) in the presence of weak disorder (shown as an energy landscape in green -- positions on top of mountains cost a lot of energy) in a type 2 superconductor. The (nearly) hexagonal lattice emerges as the disorder from the (so-called pinning) landscape is comparatively low. Several movies of this system are available. 
Figure 2 An amazing variety of new possibly particle configurations has found very recently (Dec 2012, figure 4 in http://arxiv.org/abs/1212.1130) for a set of interacting particles. All particles interact with all other particles. As a function of distance, the force is repulsive for very short distances, attractive for intermediate distances, and repulsive for very long distances. By varying the range of the attractive force (or, equivalently, changing the density of particles in the 2d simulation cell), the different particle arrangement patterns emerge. The preprint is available as pdf and allows to zoom into the vector graphics to see the details of the patterns. 
Figure 3 In a type 1.5 superconductor attraction at short distance and repulsion at long distances can lead to emergence of stripes of vortices (which arrange in a hexagonal array); taken from Phys Rev B 84 014515 (2011). The open circles are very strong pinning centres (reflecting strong damage to the superconducting sample at that point): we can see that individual vortices are captured by these pinning centres. 
Figure 4 For a different magnetic field (and thus a different average vortex particle density, and a different average vortex spacing) in the same type 1.5 superconductor emergence of superclusters can be observed. (Source: Phys Rev B 84 014515 (2011)) If you wish to discuss any details of the project informally, please contact Hans Fangohr, CED research group, Email: h.fangohr@soton.ac.uk, Tel: +44 (0) 2380 59 8345 Application deadline: applications are invited as soon as possible Please contact Hans Fangohr <fangohr@soton.ac.uk> for informal queries, expressions of interest or applications.
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