拓扑量子物态的物理概念最近被引入声子体系，由此演生出一个新兴研究方向—拓扑声子学，即利用Berry相位、赝自旋、拓扑等新奇量子自由度实现全新的声子操控，对未来声子学基础理论与器件应用的发展有重要意义。目前已被发现的拓扑声子态种类还很有限，且当前研究以理论模型为主，缺少相应的实际材料用于后续实验。基于我们已有的前期工作积累，本项目将针对上述前沿领域中的关键科学问题开展如下三方面的理论工作：1）探索声子体系中的新奇拓扑量子物态，特别是无需破坏时间反演对称、受晶格对称保护且易于在实际固体材料中实现、具有二维或三维非平庸拓扑特性的声子态（如拓扑绝缘态、拓扑Dirac或Weyl半金属态）；2）探讨对称性与声子拓扑的相互作用以及对称性破缺对声子特性的调制，探索新型的拓扑声子量子效应，并设计潜在的器件应用；3）结合第一性原理材料计算，预测具有非平庸拓扑声子态的实际材料体系，为后续实验与应用研究提供指导。

Recently physical concepts of topological states of quantum matter have been introduced into phononic systems, leading to the emergence of a new research direction—topological phononics, which utilizes novel quantum degrees of freedom (like Berry phase, pseudospin and topology) for controlling phonons in unprecedentedly new ways. The research of this emerging field is of crucial importance to develop fundamental theory and practical applications for future phononics. However, despite some early preliminary findings, only very limited types of topological phononic states have been discovered until now. Moreover, current research predominately focused on studying theoretical models, but little progress has been achieved in finding desirable real materials for experimental research. In this context, our project is aim to solve the above key scientific problems of the cutting-edge field, based on our own previous progresses of this field. We plan to perform theoretical works on the following three aspects: 1) Explore novel topological quantum states of phononic systems, especially those phononic states with no need of breaking time reversal symmetry, protected by crystalline symmetries, easily realized in real solid-state materials, and characterized by two- or three-dimensional nontrivial topological invariants (e.g. topological insulator-like states, topological Dirac or Weyl semimetal-like states); 2) Study the interplay of symmetry and topological phonons together with the influence of symmetry breaking, explore exotic topological quantum effects of phonons and further try to design promising device applications; 3) In combination with first-principles material simulation, predict real material systems that host topologically nontrivial phononic states, and provide useful guidance for following experiments and applications.