Non-Hermitian Topological Magnonics

The topology of the states can be characterized topologically by considering the accumulation of edges and corners. This can be done under periodic boundary conditions, where energy is a function of two real wave vectors, κ one and κ two. A winding number and value tuple can be defined in this context. For example, to calculate W one, κ two is fixed and the energy vector is a function of κ one. By evolving the wave vector of κ, W one can be determined in the first Brillouin zone. Similarly, to calculate W two, κ one is fixed and κ two evolves in the first Brillouin zone. This approach allows for the identification of edge accumulation.