  Wave scattering structures with amplification and dissipation can be modelled
by non-Hermitian systems, opening new ways to control waves at small length
scales. In this work, we study the phenomenon of topologically protected edge
states in acoustic systems with gain and loss. We demonstrate that localized
edge modes appear in a periodic structure of subwavelength resonators with a
defect in the gain/loss distribution, and explicitly compute the corresponding
frequency and decay length. Similarly to the Hermitian case, these edge modes
can be attributed to the winding of the eigenmodes. In the non-Hermitian case,
the topological invariants fail to be quantized, but can nevertheless predict
the existence of localized edge modes.
