准晶及非晶体系拓扑态和新奇拓扑效应的理论研究

拓扑态和拓扑材料因其新奇的拓扑效应，丰富的物理内涵及广阔的应用前景，在最近十几年里发展迅速，并成为国际前沿科学的重要研究热点。但迄今为止大多数拓扑体系都基于晶体材料，对于准晶和非晶等具有特殊结构和物性的体系中的拓扑物理却一直缺乏系统而深入的研究。本项目中，我们将着重研究准晶和非晶体系中的拓扑态和新奇拓扑量子效应。我们将发展适用于判定准晶和非晶体系拓扑性质的新型理论和方法，并预测和设计准晶和非晶拓扑材料。同时，针对准晶这种介于晶体和非晶之间的独特物质形态，我们将深入探索受特殊准晶对称性保护且准晶所独有的拓扑态，以及相位子等准晶中独特的元激发导致的拓扑量子效应。此外，通过对比晶体和非晶体中的拓扑态，我们还将系统地研究缺陷、掺杂和无序等因素对材料拓扑性质的影响，为拓扑材料制备和实际应用开发提供有益的指导。通过上述问题的研究，我们将系统全面地认识准晶和非晶体中微观结构特征与其拓扑物性的关联。

Due to its unique new effects, rich physical connotation and broad application prospects, topological states and materials have made significant progress in the last decade and have become an important research focus in international frontier science. However, most of the topological systems studied up to now are based on crystalline materials, topological states in quasicrystalline and amorphous systems which have special structures and physical properties are far from well investigated. In this project, we will focus on topological states and novel topological phenomena in quasicrystalline and amorphous systems. We will develop new theories and efficient methods to determine the topological properties of quasicrystalline and amorphous systems. Based on these new approaches, we will predict and design quasicrystalline and amorphous topological materials. Beyond the classical crystallographic restriction of periodicity, we will explore the unique topological states which are protected by special quasicrystalline symmetry. Meanwhile, we would also like to investigate novel topological quantum effects that are induced by unique excitations in quasicrystals, such as phasons. In addition, by systematically comparing topological states in crystalline and amorphous systems, we will study the effects of defects, doping as well as amorphization on topological properties of materials, providing useful guidance for experimental synthesis and practical application of topological materials. Through this research project, we aim to understand the connection between microstructural feathers and topological properties of quasicrystalline and amorphous systems.