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

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