Non-Hermitian Topological Magnonics

The magnon mode in the ferromagnet is coupled with the photon mode, resulting in a non-Hermitian Hamiltonian. The non-Hermitian Hamiltonian is defined by the coupling constants. After the hybridization of the magnon and photon modes, two frequencies are obtained: omega up and omega down. These frequencies are determined by a specific equation. The question arises as to why the square roots can be zero, and if so, we can identify the nodal magnon-photon parameter.