Proper Definition of Intrinsic Nonlinear Current

We show that the three commonly employed approaches that define the same dc (or low-frequency) intrinsic linear anomalous Hall response actually lead to different results for intrinsic nonlinear transport. The difference is due to an intrinsic anomalous distribution (IAD). It originates from a nonlinear field effect during scattering, but its value is completely independent of scattering, because it represents the local equilibration of electron wave packets with field corrected energy. The proper definition of intrinsic current that is detectable in experiment must incorporate the effect of IAD. We also show that IAD is indispensable for consistency with fundamental physical relations. In addition, we predict that under ac driving, the intrinsic reponses in rectified and double-frequency channels exhibit distinct frequency dependence, for which we estimate the signals that can be probed in antiferromagnetic CuMnAs.