论文标题
在更高维度中构建高阶拓扑状态
Constructing higher-order topological states in higher dimension
论文作者
论文摘要
高阶拓扑阶段作为浆果阶段的概括吸引了大量研究。但是，当前支持高阶拓扑阶段的当前理论模型在将晶格从较低的维度延伸到更高维度时不能给出较低和高阶拓扑阶段之间的联系。在这里，我们从理论上提出并在实验上证明了从边缘状态构建的拓扑角状态。二维方晶格在每个方向上都具有独立的耦合耦合的空间调制，并且每个方向的边缘状态的组合在二维晶格中呈现到高阶拓扑角状态，揭示了较低和更高尺寸的lattices中拓扑相之间的连接。此外，二维晶格中的拓扑角状态也可以看作是以矢量Chern数为特征的四维拓扑阶段减少尺寸，考虑到两个调制阶段是Aubry-Andre-Harper模型中的合成维度，在此处在此处讨论。我们的工作深入了解拓扑阶段的理解，突破了晶格维度，并提供了一种有前途的工具，该工具在更高的维度结构中构建了更高的拓扑阶段。
Higher-order topological phase as a generalization of Berry phase attracts an enormous amount of research. The current theoretical models supporting higher-order topological phases, however, cannot give the connection between lower and higher-order topological phases when extending the lattice from lower to higher dimensions. Here, we theoretically propose and experimentally demonstrate a topological corner state constructed from the edge states in one dimensional lattice. The two-dimensional square lattice owns independent spatial modulation of coupling in each direction, and the combination of edge states in each direction come up to the higher-order topological corner state in two-dimensional lattice, revealing the connection of topological phase in lower and higher dimensional lattices. Moreover, the topological corner states in two-dimensional lattice can also be viewed as the dimension-reduction from a four-dimensional topological phase characterized by vector Chern number, considering two modulation phases as synthetic dimensions in Aubry-Andre-Harper model discussed as example here. Our work deeps the understanding to topological phases breaking through the lattice dimension, and provides a promising tool constructing higher topological phases in higher dimensional structures.
