Moire系统平带中的拓扑及电子关联特性研究

目前对魔角双层石墨烯及类似的Moire体系中观测到的关联绝缘相、超导相等新奇物理现象尚缺乏合理的理论解释。种种实验结果表明该类体系同时具有拓扑及强关联特性，这给理论研究带来了诸多挑战。为理解不同的物理相、厘清各种相产生机制、拓扑相变发生的可能、超导产生的机理及其性质，本项目将主要从以下几个方面展开：.1 掺杂情况下体系所处铁磁关联绝缘态的特性及其产生机制，尤其是3/4掺杂体系是研究重点；.2 3/4掺杂体系可能存在两种拓扑相变机制。在体系或与六角氮化硼基底对齐，或处于手征极限时，其基态均表现出量子反常霍尔效应。我们将通过对这两种情况的研究，深入理解体系从拓扑相过渡到铁磁拓扑平庸绝缘相的过程；.3 讨论电-声相互作用，电子-电子相互作用等超导产生机制以及考察不同机制下超导的不同特性。.在以上研究的基础上，我们将把研究结果推广到其他Moire系统中，以期更好地理解拓扑与强关联之间的相互影响。

Since the discovery of correlated insulating phases and superconductivity (SC) in magic-angle twisted bilayer graphene and other Moire systems, many other novel phenomena have been observed in subsequent experiments, indicating exotic physics in such systems. Motivated by these experiments, theorists start to reveal the critical role of both nontrivial topological properties and the strong interactions in understanding the features of these correlated states. In this proposal, we will investigate this system mainly from the following perspectives:.1..the properties and the mechanism of the insulating phases observed at the odd fillings, especially when each unit cell contains one hole. The experiments discover a ferromagnetic insulating state with trivial topological properties. Such a state cannot fit into the picture of quantum Hall ferromagnetism that has been believed to be closely related to the insulating states found at even fillings..2..the properties of the topological phase transition. The quantum anomalous Hall (QAH) state has been identified at the same filling when the system aligns with the hBN substrate or is in the chiral limit. We will investigate the topological phase transition between QAH and the topological trivial ferromagnetic state..3..the mechanism of the SC in this system, such as electron-phonon or electron-electron interactions, and the corresponding properties of SC. .Our study will provide not only an understanding of the various phases in Moire systems but also a more general perspective to study the electron correlations in topological electron systems.