Nonlinear Hall Effect with Time-Reversal Symmetry: Theory and Material Realizations

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. As a second response, however, Hall dissipationless transverse currents can appear even in time-reversal symmetric conditions provided the material is non-centrosymmetric. This non-linear Hall 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, the general theory underpinning this effect is reviewed and various material platforms where non-linear Hall transverse responses have been found are discussed. 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.