Population III Supernovae as a dust factory I --- molecule formation and mixing/fallback in ejecta

Recent observations have revealed the spectral feature of carbonaceous grains even in a very distant galaxy. We develop a state-of-the-art dust synthesis code by self-consistently solving molecule and dust formation in supernova (SN) ejecta that contain various elements in different layers. With a progenitor mass 25 Msun and explosion energy 10^{52} erg, we run the following four test calculations to investigate the impact of input physics. (i) With molecule formation solved, our SN model produces 8.45x10^{-2} Msun carbonaceous grains. (ii) If all available C and Si were initially depleted into CO and SiO molecules, respectively, the C grain mass could be underestimated by ~40%. In these two models producing 0.07 Msun 56Ni without mixing fallback, a large amount of silicates (0.260 Msun) created in O-rich layers are also ejected and likely to hide the spectral feature of carbonaceous grains. We then consider mixing-fallback that can reproduce the observed elemental abundance ratios of C-normal and C-enhanced extremely metal-poor stars in the Milky Way. (iii) In the former, the mass ratio of carbonaceous to silicate grains is still small (~0.3). However, (iv) in the latter (known as a ``faint SN'), while the C grain mass is unchanged (6.78x10^{-2} Msun), the silicate mass is reduced (9.98x10^{-3} Msun). Therefore, we conclude that faint SNe can be a significant carbonaceous dust factory in the early Universe.