Systematic Study of Structural Phase Transitions based on a New Electron Theory of Solids

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We have investigated the following two subjects in this period: The first subject is the electron problem in low dimenstional materials, namely electronic states in incommensurate charge density waves (CDW) are studied, focusing on its energy gap structure. We have found a peculier gap structure characteristic of incommensurability. We also studied CDW under applied fields and the spin-peierls systems under high fields. Numerical calculations on quasi-periodic systems have been done in connection with the incommensurability problem to know the localization in this system. We have obtained a new power law behavior in the eigenvalue distribution.The second subject is the superconductivity in heavy electron materials. In order to uncover the nature of the exotic superconducting pairing states observedwe have considered the relationship between superconductivity and antiferro-magnetism and we have classified group-theoretically possible pairing states. By combining these two methods most plausible pairing states realized in UPt_3, UBe_<13> and URu^2Si_2 are enumerated. This prediction should be checked experimentally in near future.We have proposed a mechanism for high-Tc in recent oxide superconductors which shares common feature as a highly correlated system with the above heavy electron materials.