Fig. 1: Illustration of corrections to the AHE conductivity in the presence of an electric field (Ex).
From: General nonlinear Hall current in magnetic insulators beyond the quantum anomalous Hall effect
a Velocity shift of the wave packet due to the transition between the occupied (n) and unoccupied (m) bands. b Positional shift of a wavepacket due to interband transitions. c Berry curvature renormalization by the third bands. All three contributions (see Eqs. (4), (5), and (6)), which are linear in Ex, are non-zero for a generic multiband dispersion which breaks both inversion and time-reversal symmetries.
