Unconventional Superconductivity and Magnetism in Strongly Correlated Electron Systems

1.对Sr_2RuO_4中自旋三重态超导态的理论研究。第一个重要步骤是库珀对对称性的确定。实验证明，该配对通道是奇宇称、自旋三重态，并破坏了时间反转对称性。具有这些对称性的Sr2RuO4超导态的最有希望的候选者是所谓的Px+Ipy型手征p波态，类似于超流的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波态稳定性的微观来源，阐明了自旋-轨道耦合和多轨道电子结构的关键作用。研究了手性p_x+ip_y对称性的一些现象。它们包括(1)约瑟夫森效应，(2)界面、杂质周围或内部涡旋的准粒子谱，以及(3)自发霍尔效应。另一个重要的问题是发展了所谓的3-Kelvin相的现象学，3-Kelvin相是含Ru金属夹杂物的Sr2RuO4中的一种非均匀超导相。提出了具有自旋-轨道耦合的二维双交换系统中非常规超导电性的机制。研究了具有铁磁和反铁磁交换耦合的随机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重新计算。我们已经解析地证明了键序状态的存在。

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.