Theory of Superconductivity in Correlated Electron Systems

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A program of braodly-based theoretical research into superconductivity is proposed, ranging from the microscopic description of the superconductive mechanism in high-Tc superconductors to the investigation of flux-pinning in high- field Niobium-Titanium superconducting magnets. In the microscopic work, the approach is to construct variational wavefunctions for the ground and excited states of the two- dimensional Hubbard model. The investigator has recently found an expression for the excited states, building on earlier work for the ground state. The energy and other properties of these can be evaluated using a numerical technic previously developed by the investigator and others. They also propose to continue to develop the analytic theory of this model to finite temperatures, using a recently discovered mapping of the entropy into a well- understood statistical mechanical problem. Further work aimed at determining the microscopic phase of UPt3 using experimental neutron-scattering data as input will be pursued. Collaboration with experimental groups at Wisconsin will also continue. The model of granular superconductivity to explain properties of weakly-connected superconductors will be explored by numerical methods. Numerical solutions of the Ginsburg-Landau equations for different flux-pinning morphologies (experimentally determined) will be obtained.. These last two projects will help to optimize the properties of oxide and Niobium-Titanium magnets.