  Topology is quickly becoming a cornerstone in our understanding of electronic
systems. Like their electronic counterparts, bosonic systems can exhibit a
topological band structure, but in real materials it is difficult to ascertain
their topological nature, as their ground state is a simple condensate or the
vacuum, and one has to rely instead on excited states, for example a
characteristic thermal Hall response. Here we propose driving a topological
magnon insulator with an electromagnetic field and show that this causes edge
mode instabilities and a large non-equilibrium steady-state magnon edge
current. Building on this, we discuss several experimental signatures that
unambiguously establish the presence of topological magnon edge modes.
Furthermore, our amplification mechanism can be employed to power a topological
travelling-wave magnon amplifier and topological magnon laser, with
applications in magnon spintronics. This work thus represents a step toward
functional topological magnetic materials.
