Strain-induced boundary states and phase transitions in photonic graphene flakes

Strain has been extensively employed to tailor graphene’s properties and has emerged as a powerful tool for engineering gauge fields and exploring fundamental phenomena in artificial platforms such as photonic graphene. Here, we uncover that in graphene flakes with custom boundaries, uniaxial strain can be used to selectively create or eliminate edge states, depending on the strain direction. This is experimentally demonstrated in a photonic platform with two specific examples: one flake structure with pairs of twig and zigzag edges, and the other with pairs of armchair and bearded edges. We find that the existence of the edge states and their positions in momentum space are accurately predicted by appropriate winding numbers, unveiling the underlying topology of such edge states. Furthermore, when a graphene flake supports the maximum number of edge states along its boundaries after a semimetal-to-insulator transition, both compact localized edge states and corner states emerge, signaling the realization of a photonic “minimal-model” higher-order topological insulator. Our results establish strain as a versatile knob for boundary-state engineering and higher-order topology in graphene-based systems.