Non-Hermitian Topological Magnonics

Constructing the periodic boundary condition for long-range interactions can be complicated. It is necessary to repeat the area for an infinite system and define a large Hamiltonian. Despite these challenges, we were able to find an analytical solution for the energy. When the wave vector evolves from minus π to π, the energy vector forms a closed circle, as shown in a movie. This evolution of the wave vector from minus π to π results in a closed circle, indicating an integer value number and no significant Hermitian effect. In our further exploration, we extended the one-dimensional array to a two-dimensional case with various shaped magnets. We anticipate that the magnon states may accumulate under the edge of the column.