Localization and Critical Phenomena in Disordered Media

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Research will be conducted on properties of flux lines in superconductors and on localization, multiple scattering and interference of waves in disordered media. For the first topic, investigations will be undertaken on the nature of the quasiparticle excitations in the mixed state of a type II superconductor with a view to determining whether de Haas van Alphen oscillations can be observed and thus provide information on the Fermi surface of high temperature superconductors. Research will also be undertaken on the properties of disordered flux line arrays near the upper critical field using an appropriate variational order parameter. The properties of flux lines in thin films with applied field parallel to the surface will also be studied with the objective of understanding recent vibrating reed experiments. For the second topic, localization of light, the scattering of light by a disordered medium will be studied when the scattering is predominately small angle scattering. This approach leads to some interesting simplifications. The behavior appears to be dominated by interference effects. Understanding and calculating these effects is one objective of the proposed research. %%% The research conducted on this grant focusses on two areas of current interest in condensed matter and materials physics. In the first area, the fundamental properties of magnetic flux lines in type II superconductors, such as the recently discovered high temperature superconductors, will be studied. While the properties of flux lines and the structures which they form are of basic importance to the underlying physics of these superconductors, they are also of great importance to the production of real superconducting materials which have high current densities. The second area of research is the localization of waves by disorder. It has long been known that electrons travelling in disordered media, such as an amorphous semiconductor, can be localized due to the intrinsic disorder in the material. Of more recent interest is the discovery of the localization of electromagnetic waves (light) by disordered materials. This opens up the possibility of designing materials which treats light in the same way as semiconductors, say, deal with electrons. Basic research in this area can have a large impact on the design and use of photonic materials.