Non-Hermitian Topological Magnonics

When the effective Hamiltonian is not Hermitian, the resulting energy spectra are generally not real, containing both real and imaginary parts. This structure allows for a new characterization of topology. In the Hermitian case, wave functions are used to characterize topology, known as wave function topology. For example, Berry phase is used to calculate Berry curvature and the Chern number. However, in the non-Hermitian case, there is some freedom in the energy spectrum that can also play a role. This freedom can be used to define spectral quantities. By evolving some parameters in this space, energy spectra can form structures. This allows for the definition of spectral winding numbers or energy vorticity to characterize non-Hermitian topology. I will provide examples to explain this point later.

Based on non-Hermitian topology, many exciting phenomena have been discovered.