  Imaging of the dust continuum emitted from disks around nearby protostars
reveals diverse substructure. In recent years, theoretical efforts have been
intensified to investigate how far the intrinsic dynamics of protoplanetary
disks (PPDs) can lead to such features. Turbulence in the realm of non-ideal
magnetohydrodynamics (MHD) is one candidate for explaining the generation of
zonal flows which can lead to local dust enhancements. Adopting a radially
varying cylindrical disk model, and considering combinations of vertical and
azimuthal initial net flux, we perform 3D non-ideal MHD simulations aimed at
studying self-organization induced by the Hall effect in turbulent PPDs. To
this end, new modules have been incorporated into the NIRVANA-III and FARGO3D
MHD codes. We moreover include dust grains, treated in the fluid approximation,
in order to study their evolution subject to the emerging zonal flows. In the
regime of a dominant Hall effect, we robustly obtain large-scale organized
concentrations in the vertical magnetic field that remain stable for hundreds
of orbits. For disks with vertical initial net flux alone, we confirm the
presence of zonal flows and vortices that introduce regions of super-Keplerian
gas flow. Including a moderately strong net-azimuthal magnetic flux can
significantly alter the dynamics, partially preventing the self-organization of
zonal flows. For plasma beta-parameters smaller than 50, large-scale,
near-axisymmetric structures develop in the vertical magnetic flux. In all
cases, we demonstrate that the emerging features are capable of accumulating
dust grains for a range of Stokes numbers.
