Topological Invariants in Point Group Symmetric Photonic Topological   Insulators
  We proposed a group-theory method to calculate topological invariant in bi-isotropic photonic crystals invariant under crystallographic point group symmetries. Spin Chern number has been evaluated by the eigenvalues of rotation operators at high symmetry k-points after the pseudo-spin polarized fields are retrieved. Topological characters of photonic edge states and photonic band gaps can be well predicted by total spin Chern number. Nontrivial phase transition is found in large magnetoelectric coupling due to the jump of total spin Chern number. Light transport is also issued at the {\epsilon}/{\mu} mismatching boundary between air and the bi-isotropic photonic crystal. This finding presents the relationship between group symmetry and photonic topological systems, which enables the design of photonic nontrivial states in a rational manner. 
Xiao-Dong Chen, Zi-Lan Deng, Wen-Jie Chen, Jia-Rong Wang, and Jian-Wen   Dong
physics.optics cond-mat.mes-hall