  Plasmas have been recently studied as topological materials. However, a
comprehensive picture of topological phases and topological phase transitions
in cold magnetized plasmas is still missing. Here we systematically map out all
the topological phases and establish the bulk-edge correspondence in cold
magnetized plasmas. We find that for the linear eigenmodes, there are 10
topological phases in the parameter space of density $n$, magnetic field $B$,
and parallel wavenumber $k_{z}$, separated by the surfaces of Langmuir wave-L
wave resonance, Langmuir wave-cyclotron wave resonance, and zero magnetic
field. For fixed $B$ and $k_{z}$, 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 type of edge modes is given and
verified by numerical solutions. 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.
