Photonic Weyl semimetals in pseudochiral metamaterials

We investigate the photonic topological phases in pseudochiral metamaterials characterized by the magnetoelectric tensors with symmetric off-diagonal chirality components. The underlying medium is considered a photonic analogue of the type-II Weyl semimetal featured with two pairs of tilted Weyl cones 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 vacuum and the pseudochiral metamaterial exist in their common gap in the wave vector space, which are analytically formulated by algebraic equations. In particular, the surface modes are tangent to both the vacuum light cone and the Weyl cones, which form two pairs of crossing surface sheets that are symmetric about the transverse axes. At the Weyl frequency, the surface modes that connect the Weyl points form four Fermi arc-like states as line segments. Topological features of the pseudochiral metamaterials are further illustrated with the robust transport of surface modes at an irregular boundary.