Wave topology and topological waves in Hall MHD plasmas

The topological property of waves in fluids and plasmas has recently been an emerging research topic. It connects the existence of some surface waves in a nonuniform region to the topology of plane waves in a uniform region. Cold plasma waves are shown to have non-trivial topology [1-2], thereby supporting the so-called topological Langmuir-cyclotron waves [3-4]. Here we present the study of topological properties in Hall-magnetohydrodynamics (HMHD) models, where the electron and ion flows are not bounded to each other, and the Hall term is included in Ohm's law. The bulk waves are studied analytically in a uniform system; degeneracy points are shown to exist in the dispersion relation and support non-trivial topology. Topological surface waves are calculated numerically in a 1-D nonuniform HMHD equilibrium, which is accurately predicted by the bulk-edge correspondence principle. Furthermore, we also show that in a 1-D equilibrium, the HMHD system is PT-symmetric and exhibits a purely real spectrum when the PT-symmetry is unbroken, despite its non-Hermicity. The result of HMHD wave topology can be generalized to generic weakly nonuniform PT-symmetric systems.