Parabolic Hall effect due to copropagating surface modes

Abstract

Real-space separations of countermoving 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 countermoving bulk states, realized, e.g., in Weyl metals with intrinsically or extrinsically broken inversion and time-reversal symmetries. In this Rapid Communication we show that these copropagating surface modes are associated with a specific Hall effect-a parabolic potential profile in the direction perpendicular to and in its magnitude linear in the applied field. While in two-dimensional (2D) systems the parabolic potential profile is directly measurable, in 3D the resulting voltage between the 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.