  Several models of physics beyond the Standard Model predict the existence of
dark photons, light neutral particles decaying into collimated leptons or light
hadrons. This paper presents a search for long-lived dark photons produced from
the decay of a Higgs boson or a heavy scalar boson and decaying into displaced
collimated Standard Model fermions. The search uses data corresponding to an
integrated luminosity of 36.1 fb$^{-1}$ collected in proton-proton collisions
at $\sqrt{s} =$ 13 TeV recorded in 2015-2016 with the ATLAS detector at the
Large Hadron Collider. The observed number of events is consistent with the
expected background, and limits on the production cross section times branching
fraction as a function of the proper decay length of the dark photon are
reported. A cross section times branching fraction above 4 pb is excluded for a
Higgs boson decaying into two dark photons for dark-photon decay lengths
between 1.5 mm and 307 mm.
