Conical Diffraction from Approximate Dirac Cone States in a Superhoneycomb Lattice

Superhoneycomb lattice is an edge-centered honeycomb lattice that represents a hybrid fermionic and bosonic system. It contains pseudospin-1/2 and pseudospin-1 Dirac cones, as well as a flat band in its band structure. In this paper, we cut the superhoneycomb lattice along short-bearded boundaries and obtain the corresponding band structure. The states very close to the Dirac points represent approximate Dirac cone states that can be used to observe conical diffraction during light propagation in the lattice. In comparison with the previous literature, this research is carried out using the continuous model, which brings new results and is simple, direct, accurate, and computationally efficient.