Topological waves in cold and MHD plasmas: a perspective of spectral flow

In recent years, the topological properties of linear plasma waves have attracted increasing attention [1-5], illustrating the intriguing connection between the existence of certain surface waves in nonuniform plasma and the topology of plane waves in uniform plasma. Here, we present a rigorous description of the wave topology based on the spectral flow theorem [4, 6]. A topological mode in continuous media is understood as the spectral flow induced by the nontrivial topology of the eigenmode bundle over a sphere surrounding the phase-space Weyl point. We discuss two examples of the topological waves in cold and Hall MHD plasmas from the perspective of spectral flow. The cold plasma model is Hermitian and supports the topological Langmuir-cyclotron waves. The Hall MHD model is non-Hermitian but PT-symmetric, supporting the topological Alfvén sound wave.