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The twig edge states in graphene-like structures are viewed as the fourthstates complementary to their zigzag, bearded, and armchair counterparts. Inthis work, we study a rod-in-plasma system in honeycomb lattice with twig edgesunder external magnetic fields and lattice scaling and show that twig edgestates can exist in different phases of the system, such as quantum Hall phase,quantum spin Hall phase and insulating phase. The twig edge states in thequantum Hall phase exhibit robust one-way transmission property immune tobackscattering and thus provide a novel avenue for solving the plasmacommunication blackout problem. Moreover, we demonstrate that corner and edgestates can exist within the trivial band gap of the insulating phase bymodulating the on-site potential of the twig edges. Especially, helical edgestates with the unique feature of pseudospin-momentum locking that could beexited by chiral sources are demonstrated at the twig edges within the trivialband gap. Our results show that many topological-like behaviors ofelectromagnetic waves are not necessarily tied to the exact topology of thesystems and the twig edges and interface engineering can bring newopportunities for more flexible manipulation of electromagnetic waves.

Realization of corner and helical edge states in topologically trivial band gap by twig edge