Constructing higher-order topological states in higher dimensions

Higher-order topological phases as the generalization of Berry attract an enormous amount research. The current theoretical models supporting higher-order phases, however, cannot give connection between lower-order and when extending lattice from lower to higher dimensions. Here, we theoretically propose experimentally demonstrate a corner state constructed edge states in one-dimensional lattice. two-dimensional square owns independent spatial modulation coupling each direction, combination two directions comes up lattice, revealing phase lower- higher-dimensional lattices. Our work deepens understanding breaking through dimensions, provides promising tool constructing structures.