Constructing higher-order topological states in higher dimension

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.

arXiv comment10 pages, 9 figures

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Cited by in corpus (8)

• Topological classification of Higher-order topological phases with nested band inversion surfaces
• Hybrid-order topological odd-parity superconductors via Floquet engineering
• Generalization of Benalcazar-Bernevig-Hughes model to arbitrary dimensions
• Higher-order Skin Effect through a Hermitian-non-Hermitian Correspondence and Its Observation in an Acoustic Kagome Lattice
• Floquet higher-order topological phases in momentum space
• Boundary obstructed topological superconductor in buckled honeycomb lattice under perpendicular electric field
• Hierarchical Topological States in Thermal Diffusive Networks
• Floquet topological phases with time-reversal and space inversion symmetries and dynamical detection of topological charges