Massive metal-free stars can end their lives in a unique type of supernova, a pair-instability SN (e.g. [10, 11, 31]). Non-rotating models find that this occurs in a mass range between 140 and 260 M, where nearly all of the helium core with mass MHe 13/24 (M* - 20 M) is converted into metals in an explosion of 1051 - 1053 erg. The ejecta can be an order of magnitude greater than typical Type II SNe  and hypernovae ! The chemical abundance patterns are much different than those in typical explosions with the carbon, calcium, and magnesium yields independent of mass. These pair-instability SNe are one possible cause for carbon-enhanced damped Ly absorbers (e.g. [48, 20]).
These very energetic SNe can exceed the binding energy of halos with masses M 107 M.  investigated two explosion energies, 1051 and 1053 erg, in a cosmological halo with M ~ 106 M, neglecting any radiative feedback. Nevertheless, they found that over 90% of the gas was expelled into the IGM, and metals propagate to distances of ~ 1 kpc after 3-5 Myr. They argued that pair-instability SNe could have resulted in a nearly uniform metallicity floor in the IGM of ~ 10-4 Z at high redshifts. Subsequent works built upon this idea of a IGM metallicity floor with various techniques: (i) volume-averaged semi-analytic models [52, 74, 24], (ii) models using hierarchical merger trees [63, 50, 37], (iii) post-processing of cosmological simulations with blastwave models [35, 62], and (iv) direct numerical simulations with stellar feedback [60, 49, 39, 72].
Because blastwaves do not penetrate overdensities as efficiently as a rarefied medium, the voids will be preferentially enriched . This raises the following questions. Will the first galaxies have a similar metallicity as the IGM? How much metal mixing occurs in the first galaxies as they accrete material? The complex interplay between radiative and supernova feedback, cosmological accretion, and hydrodynamics are best captured by numerical simulations. Two groups [71, 27] showed that the enrichment from pair-instability SNe resulted in a nearly uniform metallicity in a 108 M halo at z ~ 10-15. These types of halos can efficiently cool through atomic hydrogen cooling, and the halo will form a substantial amount of stars for the first time. Both groups find that the metals are well-mixed in the galaxy because of turbulence generated during virialization [68, 28] to a metallicity Z / Z = 10-3 - 10-4. In these simulations, about 60% of the metals from SNe are reincorporated into the halo, whereas the remaining fraction stays in the IGM. In the end, Population III star formation is ultimately halted by the enrichment of the minihalos from nearby or previously hosted supernovae (SNe), marking the transition to galaxy formation.