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arXiv · 2011.11027

Constructing higher-order topological states in higher dimension

Yao Wang·Yongguan Ke·Yi-Jun Chang·Yong-Heng Lu·Jun Gao·Chaohong Lee·Xian-Min Jin
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Abstract

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.

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Yao Wang, Yongguan Ke, Yi-Jun Chang, Yong-Heng Lu, Jun Gao, Chaohong Lee, Xian-Min Jin. 2020-11-22. Constructing higher-order topological states in higher dimension. https://doi.org/10.1103/physrevb.104.224303

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