Unconventional Superconductivity and Magnetism in Strongly Correlated Electron Systems

1. Sr_2RuO_4自旋三重态超导态的理论研究重要的第一步是确定了库珀对对称性。实验表明，这种配对通道是奇宇称、自旋三重态和时间反演对称性的破坏。具有这些对称性的Sr_2RuO_4超导态最有希望的候选者是所谓的p_x + ip_y型手征p波态，它类似于超流^3He的A相。从电荷和自旋通道中的“手征”反馈效应的角度研究了手征p波态稳定性的微观起源，阐明了自旋轨道耦合和多轨道电子结构的关键作用。研究了手征p_x + ip_y对称性的一些结果。它们包括（1）约瑟夫森效应，（2）界面处、杂质周围或涡旋内部的准粒子谱，以及（3）自发霍尔效应。另一个重要的问题是所谓的3-Kelvin相现象的发展，这是一种在含有Ru金属的Sr_2RuO_4中的非均匀超导相。提出了一种自旋轨道耦合的二维双交换系统的非常规超导机制.研究了具有铁磁和反铁磁交换耦合的无规自旋链的有限温度热力学和零温自旋关联.对一维扩展Hubbard模型的基态相图进行了半填充的重新研究。我们已经用解析的方法证明了键序态的存在。

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.