  The twig edge states in graphene-like structures are viewed as the fourth
states complementary to their zigzag, bearded, and armchair counterparts. In
this work, we study a rod-in-plasma system in honeycomb lattice with twig edge
truncation under external magnetic fields and lattice scaling and show that
twig edge states 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 the negative permittivity background exhibit robust one-way transmission
property immune to backscattering and thus provide a novel avenue for solving
the plasma communication blackout problem. Moreover, we demonstrate that corner
and edge states can exist within the shrunken structure by modulating the
on-site potential of the twig edges. Especially, helical edge states with the
unique feature of pseudospin-momentum locking that could be excited by chiral
sources are demonstrated at the twig edges. Our results show that the twig
edges and interface engineering can bring new opportunities for more flexible
manipulation of electromagnetic waves.
