若干超导体系中关联效应的相关理论研究

      在超导系统中，电子关联效应有非常重要的影响。本文研究了几种关联效应较强且关注度较高的超导体系中的关联效应，这些研究可以对超导体的微观理论提供帮助，还可以为超导材料的实验研究提供参考。

       在过去的十几年时间，凝聚态物理学家对低维超导–量子点系统的兴趣急剧增加。超导–量子点体系中主要存在两个物理过程：磁性杂质与巡游电子产生近藤屏蔽效应、磁性杂质与库柏对散射诱导形成 Yu-Shiba-Rusinov 束缚态。将超导电极换成 Ising 超导体，Ising 型的自旋轨道耦合会对其产生显著影响。我们利用解格林函数运动方程的方法，研究了 Ising 超导–量子点体系中的多体关联效应。我们的结果表明此时系统的基态行为由 Ising 超导电性和近藤效应竞争主导，主要由 Ising 自旋轨道耦合强度 𝐼𝑠𝑜 和化学势 𝜇 决定。具体的，在电子型掺杂系统中，当 𝐼𝑠𝑜 ⩽ 𝜇 时，随着 Ising 自旋轨道耦合的增大，近藤效应被抑制，系统倾向于表现 Yu-Shiba-Rusinov 束缚态的行为；相反，当 𝐼𝑠𝑜 > 𝜇 时，随着 Ising 自旋轨道耦合的 增大，超导配对更容易被破环，系统倾向于表现近藤单态行为。同时，我们发现空穴型掺杂系统的情况和电子型掺杂完全相反。

       铜氧化物超导体是典型的强关联电子系统，在理论上单带的 𝑡–𝐽 模型被认为 可以抓住铜氧化物超导体中的主要物理。镍基超导体的晶体结构与铜氧化物超导体非常相似，这为非常规超导机理的研究提供了一个新的平台。有人提出镍基超导体中的超交换作用的 𝐽 值比铜氧化物超导体小，这启发我们利用密度矩阵重整化群的方法，研究了六条腿梯子晶格上的小 𝐽 情况下 𝑡–𝐽 模型系统的基态行为。我们在研究的参数范围内发现了两个条纹相和一个 SDW + CDW 相。在两个条纹相中，都存在交织的自旋密度波和电荷密度波，它们的波长与掺杂浓度相关，且自旋密度波波长为电荷密度波的两倍；在 SDW + CDW 相中，存在一个波矢固定为反铁磁波矢的自旋密度波和一个波长相对条纹相更短的电荷密度波。在三个相中均没有发现准长程超导序。我们的结果表明在更深的 Mott 区域，超导电性受到抑制， 而交织的自旋序和电荷序得到增强。

       魔角石墨烯超导体是一种新型非常规超导体。有人提出其中的超导电性是由范霍夫奇点附近的费米面嵌套驱动的，相关的绝缘态是某种密度波。这个观点在两能带模型的研究中得到了验证，但是两能带的研究模型在能态拓扑上存在问题，于是我们选用了一个能同时抓住魔角石墨烯费米能级附近的能带结构、对称性和拓扑性质的五能带模型，并利用无规相近似的方法对其进行研究。我们发现忽略能谷间微小的交换相互作用，SU(2)K × SU(2)K′ 对称性会使系统的电荷密度波和自旋密度波简并，同时超导的单态和三重态配对也会一一简并。在范霍夫奇点附近的超导配对以简并的 𝑑 波超导和 𝑝 波超导配对为主导。考虑能谷间微小的交换相互作用，电荷密度波和自旋密度波的简并性破坏，同样超导的单态和三重态配对简并性也会破坏，简并性破坏后系统的基态倾向性由交换相互作用的系数的符号决定。

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