  We study one-dimensional lattices with imaginary-valued Aubry-Andre-Harper
(AAH) potentials. Such lattices can host edge states with purely imaginary
eigenenergies, which differ from the edge states of the Hermitian AAH model and
are stabilized by a non-Hermitian particle-hole symmetry. The edge states arise
when the period of the imaginary potential is a multiple of four lattice
constants. They are topological in origin, and can manifest on domain walls
between lattices with different modulation periods and phases, as predicted by
a bulk polarization invariant. Interestingly, the edge states persist and
remain localized even if the real line gap closes. These features can be used
in laser arrays to select topological lasing modes under spatially extended
pumping.
