Sub-symmetry-protected topological states

Some topological boundary states are symmetry protected. Experiments with photonic lattices now show that the protection via sub-symmetry is enough to ensure topological modes, even if the full symmetry and topological invariant are destroyed. A hallmark of symmetry-protected topological phases are topological boundary states, which are immune to perturbations that respect the protecting symmetry. It is commonly believed that any perturbation that destroys such a topological phase simultaneously destroys the boundary states. However, by introducing and exploring a weaker sub-symmetry requirement on perturbations, we find that the nature of boundary state protection is in fact more complex. Here we demonstrate that the boundary states are protected by only the sub-symmetry, using Su-Schrieffer-Heeger and breathing kagome lattice models, even though the overall topological invariant and the associated topological phase can be destroyed by sub-symmetry-preserving perturbations. By precisely controlling symmetry breaking in photonic lattices, we experimentally demonstrate such sub-symmetry protection of topological states. Furthermore, we introduce a long-range hopping symmetry in breathing kagome lattices, which resolves a debate on the higher-order topological nature of their corner states. Our results apply beyond photonics and could be used to explore the properties of symmetry-protected topological phases in the absence of full symmetry in different physical contexts.

Automated summary

Some topological boundary states are protected by sub-symmetry, even if the full symmetry and topological invariant are destroyed. By introducing a weaker sub-symmetry requirement, researchers find that the nature of boundary state protection is more complex than previously believed. Experimental demonstrations in photonic lattices show the sub-symmetry protection of topological states and the resolution of debates on the higher-order topological nature of corner states in breathing kagome lattices. These findings have implications beyond photonics and can be applied to explore symmetry-protected topological phases in different physical contexts.