  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 $2\leq M_{\rm ini}/M_{\odot} \leq 5$ 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 10.43\log
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.
