Hybrid Monte Carlo studies of high temperature superconductors
In this thesis we have developed a Hybrid Monte Carlo simulation of the vortex state in layered high-temperature superconductors. A set of potentials that govern vortex behaviour are derived from the Lawrence-Doniach free-energy functional which incorporate (i) intra-layer coupling (ii) inter-layer Josephson and electromagnetic interactions. We develop an extensive set of system observables that enable detailed studies of the structural properties of the vortex state. Naïve truncation of the long range intra-layer potential is shown to cause incorrect physical behaviour. We present two methods to overcome the problem. The first smoothes the potential and the second performs an in-plane infinite lattice summation for the intra-layer interactions, which provides a minimum 20,000 speed-up over previous methods. We present results of the numerical B-T phase diagram in the pure and pinned sytem and obtain good agreement with available experimental and theoretical results. Significant hysteresis is observed in the melting properties of the system and we implement the Hybrid Monte Carlo (HMC) method for the first time in such a system to overcome this. The correlation time in the system and the rate of transitions between solid and liquid states are both shown to improve by a factor of 5 over the Monte Carlo (MC) method. We perform HMC simulations on a simple, well-studied model (Ryu, 1996b) and show that the HMC method accurately simulates the system. Finally we investigate the effects of a phenomenological pinning surface upon the melting properties of this system, and demonstrate that the effects of introducing disorder into the system are consistent with experimental and other numerical studies.