Quantum Planar Hall Effect in Two-Dimensional Trigonal Crystals

It is well known that the planar Hall effect (PHE) is deeply intertwined with the anisotropic magnetoresistance (AMR) characterizing strongly spin-orbit coupled materials. The amplitude of the PHE is indeed precisely set by the AMR magnitude, and vanishes when the driving electric field is aligned with the external magnetic field. Here we demonstrate that two-dimensional trigonal crystals with strong spin-orbit coupling can display a PHE of a completely different nature. This effect has a quantum origin arising from the Berry curvature of the Bloch states, and survives even when the applied current is aligned with the planar magnetic field. Moreover when the electric and magnetic fields are aligned perpendicular to a mirror line of the crystal, the PHE can occur as a second-order response at both zero and twice the frequency of the applied electric field. We demonstrate that this non-linear PHE possesses a quantum part that originates from a Zeeman-induced Berry curvature dipole.