非周期体系拓扑物态的研究进展

Research progress on topological states in aperiodic systems

最近,拓扑物态的相关研究已经从晶体扩展到非周期系统,例如准晶和非晶体系.本文结合我们研究组近期的工作,简要介绍了在非周期系统拓扑物态和拓扑相变方面的若干研究进展.首先,概括了非周期系统中拓扑物态的研究背景.随后以量子自旋霍尔效应为例,具体介绍了拓扑物态在准晶体系中的推广.由于非周期体系缺乏平移对称性,因此拓扑不变量的实空间计算方法成为判定非周期体系拓扑态的有效工具.在此基础上,进一步分析了准晶中独有的拓扑态,提出了与准晶特殊旋转对称性相容的高阶拓扑态,并构建了描述准晶中分数拓扑角模的有效模型.此外,介绍了非晶系统中的拓扑物态,重点探究了由于结构非晶化导致的拓扑相变.最后,对非周期拓扑物态的相关研究和未来可能的发展方向进行了总结和展望.

Recently,the study of topological states has been extended from crystals to aperiodic systems such as quasicrystals and amorphous systems.Several research progresses of topological states and topological phase transitions in aperiodic systems are briefly introduced in this paper based on our research group’s recent work.First,we outline the research background of topological states in aperiodic systems.The generalization of topological states in quasicrystals is then presented in detail,using the quantum spin Hall effect as an example.The real-space calculation method of topological invariants has become a vital tool for determining the topological state in aperiodic systems due to the lack of translational symmetry.We further discuss the unique topological state in quasicrystals and propose higher-order topological states compatible with the distinct rotational symmetry of quasicrystals,where an effective model is constructed to understand the fractional topological corner modes.Furthermore,we introduce topological states in amorphous systems,focusing on the structural amorphization-induced topological order.Finally,we summarize and prospect the study and possible future directions for aperiodic topological states.