Freezing of the flux liquid in high temperature superconductors

Abstract

The work presented in this thesis is concerned with examining the freezing transition of the magnetic flux lines, and the effect of this transition on the critical current. It is believed that in the region of low magnetic field the freezing line corresponds well with the so called irreversible line that appears in the H -T phase diagram of the HTcS materials. This therefore provides a useful reference to compare the results of this approach. Chapter 1 presents a general introduction to the phenomenon of superconductivity of both the conventional and high temperature superconductors. It is argued that many of the more important properties of the HTcS materials, such as the critical current, are heavily dependent on the interactions of the flux lines, and therefore the real world usefulness of these materials relies on a good understanding of their properties. In Chapter 2 a brief review of the ideas that have be put forward to explain the nature of the irreversible line is presented. Predictions made by these theories are then briefly compared with the results of recent experiments. This leads to the proposal of the irreversible line representing a freezing of the flux liquid into a flux solid. To examine the freezing transition, a relatively straightforward theory has been developed, known as density functional theory. The basis for this theory is presented in Chapter 3, and the formalism developed. The freezing of the flux lattice can then be calculated using a phenomenological form for the interaction potential of the flux lines. The results obtained for the freezing line enable a comparison between experiment and theory. In Chapter 4 an attempt to better understand the interaction potential of the flux lines is considered via a simple two-layer model. Such a model enables a better understanding of the nature of the full 3D interaction. Having calculated the interaction potential, it is then possible to repeat the calculation of Chapter 3, replacing the original phenomenological potential. The results are again compared with both experiment and earlier results. Having calculated the freezing line, the case of low magnetic field and T close to Tc is examined in Chapter 5. In this region the existence of a vortex gas is postulated. The approximate location of this state in the phase diagram is calculated, and its consequences discussed in term s of experimentally measurable effects. Finally, Chapter 6 examines the critical current by using a model of a granular superconductor. The Josephson current is calculated by finding the Green’s functions for the system in the absence of magnetic field, and then using these in a linear response theory, valid for small values of applied field. While this work has not yet been completed, preliminary results show that the calculated form of the critical current is consistent with previously published results.