Parabolic Hall Effect in Weyl Metals

A real-space separation of countermoving states to opposite surfaces is realized in various condensed-matter system, leading to different types of Hall effects, such as the quantum-, spin-, or the anomalous-Hall effect. Weyl metals with intrinsically or extrinsically broken inversion and time-reversal symmetries provide the possibility to separate a fraction of countermovers in a completely different fashion: Forward movers homogeneously distributed in the bulk and back movers localized at the surfaces. In this work we show that this special type of chiral separation is associated with a novel Hall effect --- a parabolic transverse potential profile induced by current along the magnetic field. The Hall voltage of this parabolic Hall effect is measurable in the geometry of a hollow cylinder between the inner and the outer surfaces and via associated characteristic effects in the longitudinal resistivity.