Nonlinear Hall effect with time-reversal symmetry: Theory and material realizations

TL;DR

This paper reviews the nonlinear Hall effect, a quantum phenomenon allowing transverse currents in time-reversal symmetric materials due to Berry curvature dipoles, with theoretical insights and material examples.

Contribution

It provides a comprehensive theory of the nonlinear Hall effect and discusses various material platforms where this effect has been observed or proposed.

Findings

Nonlinear Hall effect arises without breaking time-reversal symmetry.

The effect is linked to the Berry curvature dipole in materials.

Experimental verification exists in multiple material systems.

Abstract

The appearance of a Hall conductance necessarily requires breaking of time-reversal symmetry, either by an external magnetic field or by the internal magnetization of a material. However, as a second response, Hall dissipationless transverse currents can appear even in time-reversal symmetric conditions in non-centrosymmetric materials. Moreover, this non-linear effect has a quantum origin: it is related to the geometric properties of the electronic wavefunctions and encoded in the dipole moment of the Berry curvature. Here we review the general theory underpinning this effect and discuss various material platforms where non-linear Hall transverse responses have been theoretically proposed and experimentally verified. On the theoretical front, the link between the non-linear Hall effect and the Berry curvature dipole is discussed using Boltzmann transport theory. On the material front, different platforms, including topological crystalline insulators, transition metal dichalcogenides, graphene, and Weyl semimetals are reviewed.