  Plasmas have been recently studied as topological materials. We attempt at a
comprehensive picture of the topological phases, topological phase transitions,
and the bulk-edge correspondence of magnetized cold plasmas. We find that there
are 10 topological phases in the parameter space of density $n$, magnetic field
$B$, and parallel wavenumber $k_{\parallel}$. They are separated by the
surfaces of Langmuir wave-L wave resonance, Langmuir wave-cyclotron wave
resonance, and zero magnetic field. For fixed $B$ and $k_{\parallel}$, only the
phase transition at the Langmuir wave-cyclotron wave resonance corresponds to
edge modes. A sufficient and necessary condition for the existence of this new
type of edge modes is given and verified by numerical solutions. The edge modes
fall into four categories characterized by different behaviors of the Fermi
arcs or Fermi-arcs-like curves. We demonstrate that edge modes exist not only
on a plasma-vacuum interface but also on more general plasma-plasma interfaces.
This finding broadens the possible applications of these exotic excitations in
space and laboratory plasmas.
