Unconventional Superconductivity and Magnetism in Strongly Correlated Electron Systems

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1. Theoretical study on the spin-triplet superconducting state in Sr_2RuO_4. A first important step has been the identification of the Cooper pair symmetry. Experiments have concluded that the pairing channel is oddparity, spin-triplet, and breaks time-reversal symmetry. The promising candidate for the superconducting state of Sr_2RuO_4 having these symmetry properties is the so-called chiral p-wave state of p_x + ip_y type, an analog to the A-phase of superfluid ^3He. The microscopic origin for the stability of the chiral p-wave state has been examined from the point of view of "chiral" feedback effects in charge and spin channels, and the crucial role of spin-orbit coupling and the multi-orbital electronic structure has been clarified. A number of phenomena have been examined which are consequences of the chiral p_x + ip_y symmetry. They include (1) the Josephson effect, (2) the quasiparticle spectra at interfaces, around impurities or inside vortices, and (3) the spontaneous Hall effect. Another important issue has been the development of a phenomenology of the so-called 3-Kelvin phase, an inhomogeneous superconducting phase in Sr_2RuO_4 with Ru-metal inclusion.2. A mechanism of unconventional superconductivity in a two-dimensional double-exchange system with spin-orbit coupling has been proposed.3. The finite-temperature thermodynamics and the spin correlation at zero temperature in random spin chains with both ferromagnetic and antiferromagnetic exchange couplings have been studied.4. The ground-state phase diagram of the one-dimensional extended Hubbard model has been reexamined for half filling. We have shown analytically the existence of a bond-ordered state.