The Haldane Model in a Magneto-optical Honeycomb Lattice

TL;DR

This paper models a magneto-optical honeycomb lattice using a perturbed Wannier approach, revealing topologically protected modes and soliton-like wave propagation influenced by system topology and nonlinear effects.

Contribution

It introduces a tight-binding model derived from Maxwell's equations for gyrotropic rods, demonstrating topological phases and nonlinear soliton propagation in magneto-optical lattices.

Findings

Support for topologically protected edge modes with nonzero Chern numbers

Ability to switch system topology by adjusting rod radii

Observation of robust soliton-like modes in nonlinear regime

Abstract

A two-dimensional honeycomb lattice composed of gyrotropic rods is studied. Beginning with Maxwell's equations, a perturbed Wannier method is introduced which yields a tight-binding model with nearest and next-nearest neighbors. The resulting discrete model leads to a Haldane model and as such, topologically protected modes, associated with nonzero Chern numbers are supported. Changing the radii of the rods allows for the breaking of inversion symmetry which can change the topology of the system. This model 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.