Theoretical Investigations in Superconductivity and Graphene

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Superconductivity is a phenomenon occuring at very low temperatures approaching absolute zero (-273C) where certain materials lose all resistance to the flow of electrical current and become perfect conductors. First discovered in 1911, superconductivity continues to provide major theoretical and experimental challenges to the physics and materials research communities. In recent times, new classes of superconductors have been discovered at a phenomenal rate. A major breakthrough came in 1986 with the discovery of a new family of materials which superconduct at much higher temperatures than previously known. This mobilized an unprecented activity among scientists around the world due to potential for applications and improvements in existing applications using superconductivity, such as the high speed MAGLEV (Magnetic Levitation) train being implemented in Japan, superconducting cables for power transmission, microwave filers for communications, industrial magnets, and medical diagnosis with MRI (Magnetic Resonance Imaging). Many of these new superconductors are highly unconventional, posing unique difficulties with the conventional theory of superconductivity, and likely will require a new paradigm. It is expected that study of these materials will not only provide guidance as to how to develop new materials and improved properties for applications, but will also lead to new insights in to fundamental science. I have carried out research in theoretical superconductivity to further understanding of this phenomenon in both conventional and unconventional superconductors. The focus of my work is three-fold: 1) to calculate properties of superconductors for comparison with experiment; 2) to provide theoretical support for experimental groups studying superconductors; 3) to study new mechanisms for elucidating the nature of superconductivity in novel exotic superconductors, such as the high temperature superconductors. With the recent discovery of graphene, a single sheet of carbon atoms with exotic properties which may impact micro- and optoelectronics, I plan to study the optical properties and the potential for superconductivity in this and related systems.