Photonic topological phases in dispersive metamaterials.

We analyze the photonic topological phases in dispersive metamaterials which satisfy the degenerate condition at a reference frequency. The electromagnetic duality allows for the hybrid modes to be decoupled and described by the spin-orbit Hamiltonians with pseudospin 1, which result in nonzero spin Chern numbers that characterize the topological phases. In particular, the combined Hamiltonian of the hybrid modes complies with a fermionic-like pseudo time-reversal symmetry that ensures the Kramers degeneracy, leading to the topological protection of helical edge states. The transverse spin generated by the evanescent surface waves is perpendicular to the wave vector, which exhibits the spin-momentum locking as in the surface states for three-dimensional topological insulators. The topological properties of the helical edge states are further illustrated with the robust transport of a pair of counterpropagating surface waves with opposite polarization handedness at an irregular boundary of the metamaterial.