  Enhancing the local dust-to-gas ratio in protoplanetary discs is a necessary
first step to planetesimal formation. In laminar discs, dust settling is an
efficient mechanism to raise the dust-to-gas ratio at the disc midplane.
However, turbulence, if present, can stir and lift dust particles, which
ultimately hinders planetesimal formation. In this work, we study dust settling
in protoplanetary discs with hydrodynamic turbulence sustained by the vertical
shear instability. We perform axisymmetric numerical simulations to investigate
the effect of turbulence, particle size, and solid abundance or metallicity on
dust settling. We highlight the positive role of drag forces exerted onto the
gas by the dust for settling to overcome the vertical shear instability. In
typical disc models we find particles with a Stokes number $\sim 10^{-3}$ can
sediment to $\lesssim 10\%$ of the gas scale-height, provided that
$\Sigma_\mathrm{d}/\Sigma_\mathrm{g}\gtrsim 0.02$-$0.05$, where
$\Sigma_\mathrm{d,g}$ are the surface densities in dust and gas, respectively.
This coincides with the metallicity condition for small particles to undergo
clumping via the streaming instability. Super-solar metallicities, at least
locally, are thus required for a self-consistent picture of planetesimal
formation. Our results also imply that dust rings observed in protoplanetary
discs should have smaller scale-heights than dust gaps, provided that the
metallicity contrast between rings and gaps exceed the corresponding contrast
in gas density.
