Abstract
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.
Highlights
The photonic analogue of the quantum Hall (QH) states was identified in 2D gyroelectric or gyromagnetic photonic crystals[8,9,10], where the gyrotropy effect breaks the TR symmetry as a static magnetic field does in the QH system
The photonic quantum spin Hall (QSH) states were demonstrated in 2D bianisotropic photonic crystals[15,21], where the magnetoelectric coupling emulates the effect of spin-orbit interaction
The Kramers degeneracy, which is crucial to the emergence of helical edge states, cannot readily apply to the photonic system with spin 1, unless additional symmetry has been imposed in the system
Summary
Inspired by the discovery of topological insulators in recent years[1,2,3,4,5,6,7], there has been a surge of interest in the study of topological phases in photonic systems[8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23]. The counterpropagating edge modes, which are analogous to the helical edge states in the QSH system, exist in the frequency gap between the bulk bands with nonzero spin Chern numbers.
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