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 there may be edge modes even when the Chern number for each band is zero. We describe a new topological invariant which is a modified version of the chiral Floquet invariant proposed by Rudner et al. and does not require the construction of an effective Hamiltonian, and which correctly counts the number of edge modes in each spectral gap. We apply this invariant to the Kagome lattice network model and show that it includes both Chern and chiral Floquet phases.