Jackson, Damian Justin Charles
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...[Show more] 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
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.
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