Anomalous Planar Hall Effect in Two-Dimensional Trigonal Crystals.

The planar Hall effect (PHE) is the appearance of an in-plane transverse voltage in the presence of coplanar electric and magnetic fields. Its hallmark is a characteristic $\pi$-periodic, i.e. even under a magnetic field reversal, angular dependence with the transverse voltage that exactly vanishes when the electric and magnetic fields are aligned. Here we demonstrate that in two-dimensional trigonal crystals Zeeman-induced non-trivial Berry curvature effects yield a previously unknown anomalous PHE that is odd in the magnetic field and independent of the relative angle with the driving electric field. We further show that when an additional mirror symmetry forces the transverse voltage to vanish in the linear response regime, the anomalous 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 an antisymmetric quantum contribution that originates from a Zeeman-induced Berry curvature dipole.