  Protoplanetary discs are poorly ionised due to their low temperatures and
high column densities, and are therefore subject to three "non-ideal"
magnetohydrodynamic effects: Ohmic dissipation, ambipolar diffusion, and the
Hall effect. The existence of magnetically driven turbulence in these discs has
been a central question since the discovery of the magnetorotational
instability. Early models considered Ohmic diffusion only and led to a scenario
of layered accretion, in which a magnetically "dead" zone in the disc midplane
is embedded within magnetically "active" surface layers at distances ~1-10 au
from the central protostellar object. Recent work has suggested that a
combination of Ohmic dissipation and ambipolar diffusion can render both the
midplane and surface layers of the disc inactive and that torques due to
magnetically driven outflows are required to explain the observed accretion
rates. We reassess this picture by performing three-dimensional numerical
simulations that include, for the first time, all three non-ideal MHD effects.
We find that the Hall effect can generically "revive" dead zones by producing a
dominant azimuthal magnetic field and a large-scale Maxwell stress throughout
the midplane, provided the angular velocity and magnetic field satisfy Omega.B
> 0. The attendant large magnetic pressure modifies the vertical density
profile and substantially increases the disc scale height beyond its
hydrostatic value. Outflows are produced, but are not necessary to explain
accretion rates <10^{-7} Msun/yr. The flow in the disc midplane is essentially
laminar, suggesting that dust sedimentation may be efficient. These results
demonstrate that, if the MRI is relevant for driving mass accretion in
protoplanetary discs, one must include the Hall effect to obtain even
qualitatively correct results.
