Theoretical Study of Exotic Superconductivity and Magnetism

在分析超导涨落效应对核磁共振弛豫率的影响的基础上，发现铜超导体配对的对称性有利于d-对称性之间的d_<xy>配对。考虑到电子对铜和氧的场外排斥力U_<pd>的影响，我们计算了转变温度对空穴数的依赖关系。在计算中，我们在强场排斥力U_d重整为准粒子态后，对U_<pd>进行RPA处理。定性分析结果与实验结果基本一致。同时发现，U_<pd>的场外斥力很容易破坏d_<x2-y2>对。在对二维金属反铁磁嵌套自旋涨落性质研究的基础上，发现铜酸盐在正常状态下观察到的“自旋间隙…More”和“自旋-电荷分离”等反常金属相，可以统一解释为自旋涨落的模-模耦合对重归一化费米表面技术嵌套时的流动局域二象图的影响。为了研究超导态下de Haas-van Alphen （dHvA）效应的性质，我们采用朗道轨道作为单粒子态的基础进行了计算。结果表明，如果配对的对称性为各向同性s波，则只能在靠近上临界场的一个非常狭窄的区域内观察到dHvA振荡。这反过来表明，在观察到远低于上临界场的dHvA振荡的情况下，应考虑费米表面上点或线上间隙消失的各向异性超导性。我们讨论了波数-空间配对和实空间配对的交叉问题，这是由于铜超导体的相干长度很短，是晶格常数的几倍，被期望位于交叉区域。批判性地分析了Nozieres & Schmitt-Rink理论在二维情况下应用的困难。结果表明，用Kosterlitz & Thouless的形式主义来处理超导跃迁是可以避免这一困难的。少

On the basis of analysis of the superconducting flusctuation effect on the NMR relaxation rate, which shows drastic decrease just above the transition temperature, it was found that the symmetry of the pairing of cuprate superconductor is favorable for d_<xy>pairing among the d-symmetry. We have performed a calculation for hole-number dependence of the transition temperature by taking into account the effect of the off-site repulsion U_<pd> between electrons on copper and oxygen. In the calculation, we follow the RPA treatment of U_<pd> after the strong on-site repulsion U_d is renormalized into the quasi-particle state. the results are in qualitative agreement with experiments. It was also found that the off-site repulsion U_<pd> easily destroy the d_<x2-y2> pairing.On the basis of research on the properties of antiferromagnetic nested spin fluctuations in 2D metals, it was found that the anomalous metallic phase observed in the normal state of cuprates, with aspects such as "spin gap … More " and "spin-charge separation", can be explained in a unified way as an effect of the mode-mode coupling of spin fluctuations on the itinerant-localized duality picuture when the renormalized Fermi surface is technically nested.In order to investigate the property of the de Haas-van Alphen (dHvA) effect in superconducting state, we have carried out the calculations adopting the Landau orbit as a basis of the single particle state. As a result, it turned out that the dHvA oscillations can be observed only in a very narrow region near the upper critical field if the symmetry of the pairing is isotropic s wave. This in turn shows that the anisotropic superconductivity, with the gap vanishing on the point (s) or line (s) on the Fermi surface, should be considered in the case the dHvA oscillations are observed well below the upper critical field.We have discussed the problem of the crossover between wavenumber-space pairing and real-space pairing being motivated by the fact that the cuprate superconductors, with very short coherence length of a few times the lattice constant, are expected to locate in the crossover region. The difficulty of the Nozieres & Schmitt-Rink theory applied to 2D case was analyzed critically. It was shown that its difficulty can be avoided when the supercounducting transition is treated in the Kosterlitz & Thouless formalism. Less