  We present a simulation of the long-term evolution of a Population III
supernova remnant in a cosmological minihalo. Employing passive Lagrangian
tracer particles, we investigate how chemical stratification and anisotropy in
the explosion can affect the abundances of the first low-mass, metal-enriched
stars. We find that reverse shock heating can leave the inner mass shells at
entropies too high to cool, leading to carbon-enhancement in the re-collapsing
gas. This hydrodynamic selection effect could explain the observed incidence of
carbon-enhanced metal-poor (CEMP) stars at low metallicity. We further explore
how anisotropic ejecta distributions, recently seen in direct numerical
simulations of core-collapse explosions, may translate to abundances in
metal-poor stars. We find that some of the observed scatter in the Population
II abundance ratios can be explained by an incomplete mixing of supernova
ejecta, even in the case of only one contributing enrichment event. We
demonstrate that the customary hypothesis of fully-mixed ejecta clearly fails
if post-explosion hydrodynamics prefers the recycling of some nucleosynthetic
products over others. Furthermore, to fully exploit the stellar-archaeological
program of constraining the Pop III initial mass function from the observed Pop
II abundances, considering these hydrodynamical transport effects is crucial.
We discuss applications to the rich chemical structure of ultra-faint dwarf
satellite galaxies, to be probed in unprecedented detail with upcoming
spectroscopic surveys.
