  The global evolution of protoplanetary disks (PPDs) has recently been shown
to be largely controlled by the amount of poloidal magnetic flux threading the
disk, which is further controlled by the poorly understood process of magnetic
flux transport. In weakly ionized gas as in PPDs, magnetic flux is largely
frozen in the electron fluid, except when resistivity is large. When the disk
is largely laminar, we show that the relative drift between the electrons and
ions (the Hall-drift), and the ions and neutral fluids (ambipolar-drift) can
play a dominant role on the transport of magnetic flux. Using two-dimensional
simulations that incorporate the Hall effect and ambipolar diffusion (AD) with
prescribed diffusivities, we show that when large-scale poloidal field is
aligned with disk rotation, the Hall effect rapidly drags magnetic flux inward
at the midplane region, while it slowly pushes flux outward above/below the
midplane. This leads to a highly radially elongated field configuration as a
global manifestation of the Hall-shear instability. This field configuration
further promotes rapid outward flux transport by AD at the midplane, leading to
instability saturation. In quasi-steady state, magnetic flux is transported
outward at approximately the same rate at all heights, and the rate is
comparable to the Hall-free case. For anti-aligned field polarity, the Hall
effect consistently transports magnetic flux outward, leading to a largely
vertical field configuration in the midplane region. The field lines in the
upper layer first bend radially inward and then outward to launch a disk wind.
Overall, the net rate of outward flux transport is about twice faster than the
aligned case. In addition, the rate of flux transport increases with increasing
disk magnetization. The absolute rate of transport is sensitive to disk
microphysics which remains to be explored in future studies.
