Anomalous planar Hall effect in two-dimensional trigonal crystals

Raffaele Battilomo,Niccoló Scopigno,Carmine Ortix

doi:10.1103/physrevresearch.3.l012006

Raffaele Battilomo, Niccoló Scopigno + Show 1 more

Open Access

https://doi.org/10.1103/physrevresearch.3.l012006

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Abstract

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.

Highlights

The Hall effect arises when the conduction electrons of a solid acquire a transverse velocity either due to an externally applied magnetic field or an intrinsic ordered magnetic structure
In this Letter, we demonstrate that 2D materials with strong spin-orbit coupling and crystalline trigonal symmetry possess a previously overlooked anomalous planar Hall effect (APHE)
In strict analogy with the nonlinear Hall effect of time-reversal invariant materials [30,31,32,33,34,35,36,37,38,39,40], we find that this nonlinear APHE has a geometric contribution that is directly related to the first moment of the Berry curvature, the so-called Berry curvature dipole [31]

Summary

Introduction

The Hall effect arises when the conduction electrons of a solid acquire a transverse velocity either due to an externally applied magnetic field or an intrinsic ordered magnetic structure. To observe a Hall response it is necessary to break beside the time-reversal invariance all mirror symmetries These conditions are immediately met in the ordinary classical Hall effect where an out-of-plane magnetic field is applied. The conducting surfaces of three-dimensional topological insulators (3DTIs) [26] have been recently shown to support a PHE [27,28] In these materials, an external planar magnetic field conspires with the spin-momentum locking of the Dirac cones to produce a strongly directional-dependent net transverse current. This effect unique to trigonal crystals, derives directly from the “bending” of the electron trajectories encoded in the geometric properties of the electronic wave functions [29]—the APHE stems from a Zeeman-induced nontrivial

Published by the American Physical Society

The Rashba term

Conclusions