  Topological defects play a central role in the formation and organization of
various biological systems. Historically, such nonequilibrium defects have been
mainly studied in the context of homogeneous active nematics. Phase-separated
systems, in turn, are known to form dense and dynamic nematic bands, but
typically lack topological defects. In this paper, we use agent-based
simulations of weakly aligning, self-propelled polymers and demonstrate that
contrary to the existing paradigm phase-separated active nematics form ${-1/2}$
defects. Moreover, these defects, emerging due to interactions among dense
nematic bands, constitute a novel second-order collective state. We investigate
the morphology of defects in detail and find that their cores correspond to a
strong increase in density, associated with a condensation of nematic fluxes.
Unlike their analogs in homogeneous systems, such condensed defects form and
decay in a different way and do not involve positively charged partners. We
additionally observe and characterize lateral arc-like structures that separate
from a band's bulk and move in transverse direction. We show that the key
control parameters defining the route from stable bands to the coexistence of
dynamic lanes and defects are the total density of particles and their path
persistence length. We introduce a hydrodynamic theory that qualitatively
recapitulates all the main features of the agent-based model, and use it to
show that the emergence of both defects and arcs can be attributed to the same
anisotropic active fluxes. Finally, we present a way to artificially engineer
and position defects, and speculate about experimental verification of the
provided model.
