Topological phase transition of the centered rectangular photonic lattice

A Cm planar photonic material (two-dimensional) including the mirror reflection symmetry is explored where in the Dirac cones appeared at the high-symmetry points of the Brillouin zone boundary. By implementing the specific perturbation on the photonic crystal (PC), topological transition can make a bridge between the trivial PC (ordinary insulator) and the topological insulator including zero and non-zero spin Chern number (Cs), respectively. The perturbation can be realized through the rotation of the Cm photonic crystal around the nonzero angle to its initial position. Therefore, breaking the mirror symmetry of the unit cell leads to mismatch of the symmetry planes of the lattice. This modification results in the directional band gap & band inversion which is the signature of the topological transitions. The mentioned PC would be suitable for examination of the unidirectional transport of light at the topological interfaces.