MHD turbulence plays a crucial role in the dust dynamics of protoplanetary discs. It affects planet formation, vertical settling and is one possible origin of the large scale axisymmetric structures, such as rings, recently imaged by ALMA and SPHERE. Among the variety of MHD processes, the magnetorotational instability (MRI) has raised particular interest since it provides a source of turbulence and potentially organizes the flow into radial structures. However, the weak ionization of discs prevents the MRI from being excited beyond 1 AU. The strong sedimentation of millimetre dust measured in T-Tauri discs is also in contradiction with predictions based on ideal MRI turbulence. In this paper, we study the effects of non-ideal MHD and winds on the dynamics and sedimentation of dust grains. We consider a weakly ionized plasma subject to ambipolar diffusion characterizing the disc outer regions (>1 AU). For that, we perform numerical MHD simulations in the stratified shearing box, using the PLUTO code. Our simulations show that the mm-cm dust is contained vertically in a very thin layer, with typical heightscale ~0.4 AU at 30 AU, compatible with recent ALMA observations. Horizontally, the grains are trapped within pressure maxima induced by ambipolar diffusion, leading to the formation of dust rings. For micrometer grains, dust and gas scaleheights are similar. In this regime, the settling cannot be explained by a simple 1D diffusion theory but results from a large scale 2D circulation induced by both MHD winds and zonal flows. Overall, our results show that non-ideal MHD effects and their related winds play a major role in shaping the radial and vertical distribution of dust in protoplanetary discs. Leading to substantial accretion efficiency, non-ideal effects also a promising avenue to reconcile the low turbulent activity measured in discs with their relatively high accretion rates.
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