Generalized Haldane model in a magneto-optical honeycomb lattice

A two-dimensional honeycomb lattice composed of gyrotropic rods is studied. Beginning with Maxwell's equations, a perturbed Wannier method is used to derive a tight -binding model with nearest and next -nearest neighbors. The resulting discrete model leads to a generalized (photonic) Haldane model that supports topologically protected modes with nonzero Chern numbers. Varying the radii of the rods breaks inversion symmetry and can change the topology of the system. This model analytically describes experimental results associated with topological waves in magneto -optical honeycomb lattices. This method can also be applied to more general Chern insulator lattices. When on -site Kerr -type nonlinear effects are considered, coherent soliton-like modes are found to propagate robustly through boundary defects.