Photonic topological semimetals in bigyrotropic metamaterials

We investigate the photonic topological phases in bigyrotropic metamaterials characterized by the gyroelectric and gyromagnetic parameters. The underlying medium is considered a photonic analogue of the topological semimetal featured with a pair of Weyl cones separated by a distance in the frequency-wave vector space. As the 'spin'-degenerate condition is satisfied, the photonic system consists of two hybrid modes that are completely decoupled. By introducing the pseudospin states as the basis for the hybrid modes, the photonic system is described by two subsystems in terms of the spin-orbit Hamiltonians with spin 1, which result in nonzero spin Chern numbers that determine the topological properties. Surface modes at the interface between two bigyrotropic metamaterials with opposite sign of the gyrotropic parameters exist in their common gap in the wave vector space, which are analytically formulated by algebraic equations. In particular, two types of surface modes are tangent to or wrapping around the Weyl cones, which form a bent and two twisted surface sheets. At the Weyl frequency, the surface modes contain a typical and two open Fermi arc-like states that concatenate to yield an infinite straight line. Topological features of the bigyrotropic metamaterials are further illustrated with the robust transport of surface modes at an irregular boundary.