Topological edge states challenge traditional notions of symmetry and control.

Researchers have challenged the traditional belief that global symmetry is necessary for the protection of topological boundary states in systems of symmetry-protected topological phase (SPT phase). They found that topological boundary states can still exist in the corresponding subspaces, protected by sub-symmetries, even if the system no longer has quantized topological invariants and some kinds of global symmetry. The study provides new ideas for the research and application of topological states in different physical backgrounds and is expected to further promote the development of topological photonics and its cutting-edge interdisciplinary fields.