关联狄拉克材料中的磁性、超导和拓扑性质的研究

The study on topological quantum states is a hot research field in condensed matter physics. The proposal is based on the interdisciplinary field of Dirac and strongly correlated electrons systems, and focuses on magnetism, superconductivity and topological properties, to explore the new physical phenomena caused by the correlation effect in the new physical system. The applicant plans to carry out the following studies in the following four aspects, including: the chiral superconductivity in two-dimensional Hubbard model; the interaction driven insulator-metal phase transition in Dirac band insulators; correlation and disorder effects in topological insulators; new quantum states in correlated Dirac and Weyl semimetals. At the same time the latest research progress will also be paid close attention and related research is carried out. The applicant is very familiar with the new physical phenomena of Dirac materials and a variety of analytical and numerical many-body techniques. In particular the master of the determinant quantum Monte Carlo method to simulate the interacting Fermi systems, reaches the international leading level. The applicant is confident to smoothly carry out the research contents, and gets important theoretical results. Under the fund of the project, the applicant will train a number of doctoral or master's degree students, extensively carry out domestic and foreign academic exchanges, and activate domestic condensed matter theory research.

拓扑量子态是凝聚态物理学中的热门研究领域。本项目面向强关联电子系统和狄拉克电子系统交叉领域--关联狄拉克系统，针对该系统的磁性、超导和拓扑性质，探索关联效应在新物理系统中引起的新物理现象。申请人计划开展以下四个方面的研究内容，包括：二维Hubbard模型中的手征超导电性；狄拉克能带绝缘体中相互作用驱动的绝缘体-金属的量子相变；二维拓扑绝缘体中的关联和无序效应；关联狄拉克、外尔半金属中的新奇物理性质。同时还将密切关注国内、外对狄拉克材料的最新研究进展，开展相关研究。申请人对狄拉克材料中的新物理现象十分了解，熟悉掌握多种解析和数值多体技术，特别是应用行列式量子蒙特卡罗方法对关联费米子系统模拟的掌握上达到国际领先水平，有信心顺利开展上述研究内容，并得到重要的理论结果。在该项目的资助下，申请人会培养多名博士、硕士研究生，广泛地开展国内、外学术交流，活跃国内的凝聚态理论研究。

关联狄拉克系统是凝聚态物理学中研究前沿，针对该系统的磁性、超导和拓扑性质，我们探索了关联效应在狄拉克系统中引起的新物理现象。我们理论上预测了小转角双层石墨烯超晶格上费米子超导配对的对称性；基于π-flux模型中的狄拉克费米子，发现了其中的新奇超导电性，给出了对半金属-反铁磁绝缘体相变的深入理解；使用行列式量子蒙特卡罗模拟研究了立方晶格上基于π-通量模型的三维狄拉克费米子中的电子关联驱动的反铁磁相变；发现了六角晶格纳米带上硬核玻色子的扩展玻色哈伯德模型上的自组织玻色畴壁等。在该项目的资助下，共发表研究论文20篇，其中Phys. Rev. B 7篇， Phys. Rev. A 2篇，Phys. Rev. Research 2篇。其中2018年发表的论文“Pairing symmetry of interacting fermions on a twisted bilayer graphene superlattice” 【Phys. Rev. B 97, 235453 (2018)】被包括Science、Nature等顶级期刊引用142次，是ESI高引文章。我们这些研究工作加深了人们对狄拉克系统这一新物理系统中的关联效应的理解，具有比较重要的科学意义。