Computational modelling of the vortex state in high-temperature superconductors

The vortex state in high temperature superconductors is investigated using computer simulations. Vortices are represented as particles and we employ Langevin dynamics to study the statics and dynamics of the system. We show that the long-range nature of the vortex-vortex interaction can result in numerical artefacts, and provide two techniques to overcome these problems: (i) using a 'smooth' cut-off which reduces the interaction force near the cut-off smoothly to zero, and (ii) an infinite lattice summation technique applicable for a K0-Bessel function interaction potential. Using these methods, we investigate a two-dimensional vortex system driven over a weak random potential. We observe the moving Bragg glass regime, and study the recently predicted critical transverse force. Our results agree with and extend other theoretical and numerical works, and provide important confirmation for the moving glass theory. We investigate the critical transverse force as a function of system size, temperature, driving force and disorder strength. We provide numerical estimates to assist experimentalists in verifying its existence. We study vortex matter in three-dimensional layered superconductors in the limit of zero Josephson coupling. The long-range nature of the electromagnetic interaction between pancake vortices in the c-direction allows us to employ a mean-field method: all attractive inter-layer interactions are described by a substrate potential, which pancakes experience in addition to the in-layer pancake repulsion. Using an averaged pancake-density, we iteratively re-compute the substrate potential. The self-consistent method converges, depending on temperature, either to a pancake lattice or a pancake liquid. We investigate different methods to perform these simulations efficiently, and compute the instability line for the transition from solid to liquid, the melting line and the entropy jump across the transition. (author)