Theory on vortex states in anisotropic superconductors with strong correlation

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We studied theoretically ab014t the anomalous behaviors of the electronic states near the vortex cores as well as the relating phenomena, using the two-dimensional t-J model in which the anisotropic superconductivity with strong correlation is realized. For this purpose we developed the programs for numerical calculations and applied them to various cases. The obtained results are summarized as follows :1. We studied the electronic states near the vortex core of high-TィイD2cィエD2 superconductors by applying the Gutzwiller approximation to the Bogoliubov-de Gennes equations. As a result, we found possibilities that an extended s-wave component and antiferromagnetic correlations are induced inside the core when the doping rate is small.2. We examined the ground state of the two-dimensional t-J model using the variational Monte Carlo simulation which was extended for the case with antiferromagnetic order parameters. It was found that the d-wave superconductivity and antiferromagnetism coexist near half filling.3. We extended the Gutzwiller approximation for studying the strong correlation, by comparing the numerical results and analytical methods. The obtained extended approximation can be easily applied to the Bogoliubov-de Gennes equations. We used this method for the cases with antiferromagnetic correlations.4. We studied the electronic states near the boundary and impurities in the t-J model, which are closely related to the vortex problem. Some new features were found about the dependence of the surface states on the shape of the Fermi surface and about the magnetic impurities.5. We investigated the stripe state in which the antiferromagnetism and d-wave superconductivity coexist using the extended Gutzwiller approximation. It was found that some impurity pinning potential is necessary to stabilize the stripe states.