【作者】 刘洋；

【导师】 蒋建华；

【作者基本信息】 苏州大学 ， 物理学， 2021， 硕士

【摘要】 对物质拓扑性质的研究源于20世纪量子霍尔效应的发现。低温二维电子气在垂直磁场下的霍尔电导呈现出阶梯式的变化,其值为一自然常数e2/h的整数倍。其后,反常量子霍尔效应,量子自旋霍尔效应的发现极大地丰富了拓扑物理学。传统量子霍尔效应的研究主要集中于拓扑边界态的鲁棒性,即体拓扑与拓扑边界的体-边对应关系。其后,国内外的研究热点又推向了具有体-边-角对应关系的高阶拓扑。对于二维高阶拓扑绝缘体,存在拓扑保护的零维角态。特别是当引入缺陷晶格时,还伴随着奇异的新性质。本文利用能带表征理论来表征光子晶体的Wannier芯,并研究了具有旋错的光子晶体晶格中的体-旋错对应关系。理论计算与实验结果表明,对于中心具有空洞的旋错晶格存在局域在旋错中心的旋错态,这种旋错局域态的出现,往往伴随着填充反常现象,并由此可以引致分数旋错电荷的概念,证明了体-旋错对应关系的存在。分数旋错电荷与体的拓扑以及晶格缺陷息息相关,它的出现,提供了区分不同高阶拓扑的方法,拓展了高阶拓扑的物理现象,为拓扑晶格绝缘体的研究打开了新的篇章。更多还原

【Abstract】 The research on the topological properties of matter originated from the discovery of the quantum Hall effect in the 20th century.The Hall conductance of the low-temperature two-dimensional electron-gas under a vertical magnetic field exhibits a stepped change,and its step is an integer multiple of a natural constant e2/h.Afterwards,the discovery of the anomalous quantum Hall effect and the quantum spin Hall effect greatly enrich the topological physics.The research on quantum Hall effect mainly focuses on the robustness of topological boundary states.The relationship between bulk topology and topological boundary can be called bulk-boundary correspondence.However,in recent years,domestic and foreign scholars have begun to focus on looking for high-order topological materials with bulkboundary-corner correspondence.For two-dimensional insulators,high-order topology support 0-dimensional corner states.High-order topological local states also exhibit novel properties in defect lattice.We characterize the Wannier center of photonic crystal with band representation theory,and then,study the bulk-disclination correspondence in photonic disclination-lattice.The theoretical calculations and experimental results prove that for the disclination-lattice with central hole,there exists bound states localized around the center of disclination.These bound states accompanied by filling anomaly can introduce the concept of fractional disclination charge,and prove the bulk-disclination correspondence.The fractional charge determined by bulk topology and the defect of lattice supports a new method to distinguish various high-order topology,enriches the phenomenon of high-order topology,and opens a new chapter on topological crystalline insulators.更多还原