Dust formation and resulting mass loss around Asymptotic Giant Branch (AGB) stars with initial metallicity in the range of $0 leq Z_{rm ini} leq 10^{-4}$ and initial mass $2leq M_{rm ini}/M_{odot} leq 5$ are explored by the hydrodynamical calculations of dust-driven wind (DDW) along the AGB evolutionary tracks. We employ the MESA code to simulate the evolution of stars, assuming an empirical mass-loss rate in the post-main sequence phase, and considering the three types of low-temperature opacities (scaled-solar, CO-enhanced, and CNO-enhanced opacities) to elucidate the effect on the stellar evolution and the DDW. We find that the treatment of low-temperature opacity strongly affects the dust formation and resulting DDW; in the carbon-rich AGB phase, the maximum $dot{M}$ of $M_{rm ini} geq$ 3 $M_{odot}$ star with the CO-enhanced opacity is at least one order of magnitude smaller than that with the CNO-enhanced opacity. A wide range of stellar parameters being covered, a necessary condition for driving efficient DDW with $dot{M} ge 10^{-6}$ $M_{odot}$ yr$^{-1}$ is expressed as the effective temperature $T_{rm eff} lesssim 3850$ K and $log(delta_{rm C}L/kappa_{rm R} M) gtrsim 10.43log T_{rm eff}-32.33 $ with the carbon excess $delta_{rm C}$ defined as $epsilon_{rm C} - epsilon_{rm O}$ and the Rosseland mean opacity $kappa_{rm R}$ in units of cm$^2$g$^{-1}$ in the surface layer, and the stellar mass (luminosity) $M$ $(L)$ in solar units. The derived fitting formulae of gas and dust mass-loss rates in terms of input stellar parameters could be useful for investigating the dust yield from AGB stars in the early Universe being consistent with the stellar evolution calculations.
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