We theoretically investigate the third-order nonlinear Hall effect by employing the quantum kinetic equation and present an analytic formula for the third-order harmonic conductivity, where the intraband and the mixed inter-band contributions caused by the external electric field as well as the multiphoton process dressed Berry curvature are unveiled. These results are applied in a two-dimensional Dirac system. We find that the third-order harmonic conductivity exhibits a crossover from the negative to positive value due to the intraband transition of the electrons in the low-frequency region,...
