铁磁超导体在磁场中的反常磁学特性

Distinctive from conventional superconductors, ferromagnetic superconductors exhibit abnormal magnetic properties, including the coexistece of ferrromagnetism and superconductivity as well as many other strange behaviors in the magnetic field. Taking two typical materials URhGe and UCoGe for example, the former shows unusual curvature in the upper critical field and the latter displays reentrant superconductivity. Such abnormal magnetic behaviors reveal the mystery of internal structures of p-wave Cooper pairs and the sensitive dependence of the p-wave superconducting state on the magnetic field. The present project intends to explore a reasonable theoretical explanation of the abnormality associated with magnetic properties, following recent experimental progress. ..The primary focus of the project will be on (1) calculating the temperature dependence of the upper critical fields for various p-wave superconducting states from both microscopic and phenomenological points of view, with the emphasis on anomalous upward and S-shaped curvatures of the upper critical magnetic field for UCoGe. (2) examining the reentrant superconductivity of URhGe in high fields and re-emergent superconductivity of UCoGe close to the magnetic quantum critical point using the models developed above, taking into account of the spontaneous magnetization and various orientations of external fields. (3) In addition, the calculations will be extended further by considering the effects of spin-orbit coupling, which might play an important role in the interplay between magnetism and superconductivity. ..We expect that the planned research leads to an improved understanding of the coexistence of ferromagnetism and superconductivity, and helps to make clear the mechanism of p-wave Cooper pairing in such superconducting material.

铁磁超导体展示出与常规超导体不同的反常磁学性质。这种反常不仅表现在铁磁性与超导电性的共存，还体现在磁场下的许多奇异行为。以当前倍受关注的URhGe和UCoGe为例：前者的上临界磁场呈现曲率反常，后者在强场下发生超导重现现象。这些反常的磁学性质，反映出p波配对超导态具有丰富的内部结构以及敏感的磁场依赖关系。本项目将结合实验进展，从理论上理解URhGe和UCoGe在外磁场下的反常磁学行为。主要内容包括：1）从微观和唯象的角度发展适于计算不同p 波超导态上临界磁场Hc2(T)的新理论，研究Hc2(T)曲线曲率反常的内在原因；2）利用新的p 波超导理论，考虑材料内部的自发磁化和外磁场的强度与取向，研究URhGe 强场下的反常超导态和UCoGe在磁性量子相变点附近超导态的特征；3）探讨自旋-轨道耦合作用对铁磁超导体磁学行为的影响。本项目的研究旨在澄清磁性超导共存态的特点，并有助于理解p波配对的机制。

本项目计划发展Sharnberg和Klemm关于p波超导体上临界磁场的理论，建立适合于铁磁超导体等非常规超导体的新理论描述方案。预期材料的晶体结构，自发磁化以及自旋-轨道耦合等因素将对材料的上临界磁场的特征有重要影响。项目的实施基本围绕着研究计划进行，初步实现了预期的主要目标。取得的主要结果如下： ..由于材料结构通常具有很强的各向异性，其费米面必然也相应的呈现各向异性。椭球形费米面一定程度地反映了材料的各向异性，并且特别适合描述具有正交晶格结构的超导材料，如URhGe。我们发展了计算具有椭球形费米面的自旋三重态配对（p波）和自旋单态配对（s波和d波）超导体在任意方向的上临界磁场的一般理论。利用Klemm-Clem变换将椭球形费米面映射成球形费米面，得到对应形式的格林函数运动方程，获得可用于描述具有任意对称性超导序参量的超导能隙方程，并进一步计算任意角度的上临界磁场。..利用上述理论，计算了正交晶格结构的铁磁超导体处于完全对称破缺p波超导态时上临界磁场随角度的变化，发现上临界磁场在磁场方向远离c轴时呈现独特的角度依赖关系，形成两个峰值，分别位于0-90度之间和90-180度之间。还研究了超导序参量具有手性SK态对称性和手性ABM态对称性的p波配对情况，发现前者临界磁场高于后者，并且展示出有随着角度改变而发生从手性态到非手性态的一级相变的迹象。相关结果可用于分析Sr2RuO4、UCoGe和CuxBi2Se3中的超导电性。还基于该理论计算了重费米子超导体Sr2RuO4和CeCu2Si2的上临界磁场，通过与实验数据进行拟合探讨了其超导配对的对称性。..另外，根据研究计划讨论了自旋-轨道耦合作用对超导态的影响，相关工作将有助于下一步发展包含自旋-轨道耦合作用的上临界磁场理论。鉴于上临界磁场本质上与磁场中带电粒子的旋转运动有关，我们还对旋转的费米和玻色气体的一般性质进行了研究，讨论了在特定几何约束下粒子流的分布情况，计算了超流玻色气体的临界旋转速度。

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