Kagome lattice network model as a chiral Floquet topological insulator

The magnetic proximity effect can open a gap in the spectrum of Dirac electrons at the surface of a topological insulator; on the other hand, topological defects in the magnetization can host topologically protected localized (isolated skyrmion) and propagating (domain walls) states. Here we argue that the electronic structure of Dirac electrons coupled to the skyrmion lattice phase in an insulating magnet (for example, Cu₂OSeO₃) can be described by the Chalker-Coddington network model (CCN) with the Kagome geometry. We study this model relying on a recent insight that CCN should be thought of as a chiral Floquet topological insulator. While in static systems the number of edge modes is completely determined by calculation of the Chern number for each energy band, in Floquet systems a chiral Floquet phase may exist in which there are edge modes even when the Chern number for each band is zero. We describe a band reconstruction procedure which allows us to show that the Dirac electrons in a Kagome geometry end up forming a Chern band.