  Real-space separations of counter-moving states to opposite surfaces or edges
are associated with different types of Hall effects, such as the quantum-,
spin-, or the anomalous Hall effect. Some systems provide the possibility to
separate a fraction of countermovers in a completely different fashion: Surface
states propagating all in the same direction, balanced by counter-moving bulk
states, realized, e.g., in Weyl metals with intrinsically or extrinsically
broken inversion and time-reversal symmetries. In this work we show that these
co-propagating surface modes are associated with a novel Hall effect --- a
parabolic potential profile in the direction perpendicular to and in its
magnitude linear in the applied field. While in 2D systems the parabolic
potential profile is measurable directly, in 3D the resulting voltage between
bulk and surface is measurable in the geometry of a hollow cylinder. Moreover,
the parabolic Hall effect leads to characteristic signatures in the
longitudinal conductivity.
