Optical Analogue of Quantum Spin Hall Effect in a Two-Dimensional   Gyrotropic Photonic Crystal
  We propose an optical counterpart of the quantum spin Hall (QSH) effect in a two-dimensional photonic crystal composed of a gyrotropic medium exhibiting both gyroelectric and gyromagnetic properties simultaneously. Such QSH effect shows unidirectional polarization-dependent transportation of photonic topological edged states, which is robust against certain disorders and impurities. More importantly, we find that such unique property is not protected by conventional time-reversal symmetry of photons obeying the Bosonic statistics but rather by the same symmetry, as electron's time-reversal symmetry. Based on the tight-binding approximation approach, we construct an effective Hamiltonian for this photonic structure, which is shown to have a similar form to that of an electronic QSH system. Furthermore, the invariant of such model is calculated in order to unify its topological non-trivial character. Our finding provides a viable way to exploit the optical topological property, and also can be leveraged to develop a photonic platform to mimic the spin properties of electrons. 
Cheng He, Xiao-Chen Sun, Xiao-ping Liu, Zi-Wen Liu, Yulin Chen,   Ming-Hui Lu, Yan-Feng Chen
physics.optics cond-mat.mes-hall