Anisotropic Dirac cone and slow edge states in a photonic Floquet lattice

Dirac cones with isotropic and linear dispersion, as in graphene, exhibit ultrahigh carrier mobility and offer an intriguing method to manipulate the behavior of particles. This concept has recently been extended to anisotropic Dirac cones with anisotropic dispersion in condensed matter, but their photonic counterparts are yet to be explored. Here, by introducing anisotropic coupling, we propose a Floquet lattice with a realistic photonic scheme that supports anisotropic Dirac cones and abundant topological phases. Under the highly anisotropic circumstances, the presence of anomalous Floquet insulators is demonstrated, where topological slow edge states are found along a specific direction. The group velocity of the edge states can be tailored continuously by adjusting the anisotropy of the lattice. These slow edge states are robust against disorders and can be harnessed for developing intriguing applications such as anisotropic devices, topological delay lines, and optical nonlinear devices.