铜氧化物超导体涡旋束缚态对称性与拓扑序

Based on a two-component Hubbard model under the single-particle occupied constraint or starting from the Gor'kov propagators equations with the crystal point group and pairing potential symmetry in mind, we will aspire to develop a model describing the pairing correlations as a function of the hole-doping level in cuprate high-temperature superconductors, from which the evolution equations for system quantum states and the self-consistent conditions are derived. Theoretical analyses and numerical simulations will be accomplished to correctly describe the vortex bound states evolution and quantum transitions in physical parameters space. The effects of the quantum confined and the competitions between different orderings on vortex core state symmetry, the edge-bulk correspondence rules will be specified, with emphasis on the symmetry and topological order of vortex core state of the hole-doped cuprate superconductors, and its basic nature. We will show whether the electromagnetic field induced phase-coherent state could be a ground state above the critical temperature or in the so-called pseudogap phase, to explore the possibilities of two-particle occupied state within the framework of the Hubbard model with large on-site repulsion, and to suggest and possible phase-coherent control approaches. We expect such in-depth and systematic investigations will provide important informations and clues in promoting ones understanding on the fundamentals physics like the conjecture of extend Anderson insulating state, and in revealing the insulator-metal transition and the high-Tc superconductivity origins in cuprate superconductors.

以双分量Hubbard模型为出发在单粒子占据的约束下或者是从 Gor’kov传播子模型出发在与系统晶格点群对称群以及对势对称性相容的前提下，试图建立描述高温超导体对关联函数随掺杂度变化的物理模型；并由此推导量子态时间演化方程和自洽迭代条件. 通过理论分析与数值模拟，正确描述在物理参量空间涡旋量子态演化过程。研究量子受限尺寸效应和多序相互作用对涡旋态的对称性的影响、边缘态-体态对应规则；将重点关注空穴掺杂铜氧化物超导体磁通涡旋态对称性与拓扑序，描述其基本属性。将回答外部电磁场作用下赝能隙区量子态相位相干与否的问题。探索Hubbard模型框架下双粒子占据的可能性、建议并论证对其量子态相位相干调控方案. 为理解与拓展Anderson 绝缘态概念相关的基本物理问题、揭示铜氧化物超导体中绝缘-金属相变及其超导电性起因提供重要启示。

本项目重点研究、描述空穴掺杂铜氧化物超导体磁通涡旋态对称性与拓扑序，分别从 Gor’kov 传播子方程和双带紧束缚模型哈密顿出发推导出相应的微观 GL方程和 BdG 方程及其自洽条件.主要研究成果包括：(1) 揭示了d-波超导环中磁场诱导的超导-绝缘相变过程和 Majorana 粒子态的存在性问题；同时，在超导/半金属结中重点考虑自旋-轨道相互作用过程以描述自旋单态配对态与奇频三重态配对态间转换机制；明确了自旋三重态零能模与界面散射的关系.(2) 描述了磁场下d波超导体的新奇量子涡旋态； 结果表明非局域散射效应，可以导致不同宇称的配对态间相互转换和 Skyrmion (斯克闵子) 涡旋以及半涡旋-反涡旋对态; 刻画了相应的织构与拓扑特征与体系的对称性和表面散射强度的依赖关系.(3) 论证了铜氧化物高温超导中自旋轨道耦合诱导的对称破缺和马约纳费米态的存在性问题。具体地，在空穴掺杂的YBCO高温超导条带系统中，合适的自旋轨道耦合和交换场强度，将诱导出零能的手征边界态。证明了该零能手性边界态对应着马约纳零能模；并揭示了利用外加磁场对其进行调控的方案.我们还发现手征边界态以及马约纳零能模在欠掺杂样品中更易于产生， 这与欠掺杂样品中相对较强的在位库仑作用诱导的交错磁化场及对称性相变有关. (4) 对d+is 波超导体的BdG方程的自洽求解，揭示了随外场和温度变化的新奇的涡旋态及其拓扑序； 其中强调了双带超导序相互竞争机制和非厄密的梯度耦合项物理过程，预言了随掺杂度而变化的新奇涡旋态、斯克闵子结构相变和分数拓扑荷现象。.这些研究成果有助于深入理解铜氧化物超导体中涡旋量子态演化与相变和欠掺杂区赝能隙的物性实质，为探索对称破缺诱导的马约纳束缚态提供可参考的路径。