Third-order nonlinear Hall effect in two-dimensional Dirac systems

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, whereas a kink or dip structure due to the multiphoton process between the conduction and valence bands in the high-frequency region. In experiment, these features can be identified by detecting the transverse current. Our work deepens the understanding of the multiphoton process in the nonlinear transport of topological materials and enlightens a possible way to its characterization in experiments.