Demonstration of the third-order nonlinear Hall effect in topological Dirac semimetal NiTe${}_2$

We experimentally investigate third-order nonlinear Hall effect for three-dimensional NiTe${}_2$ single crystal samples. NiTe${}_2$ is the recently discovered type-II Dirac semimetal, so both the inversion and the time-reversal symmetries are conserved in the bulk. As a result, the well known second-order nonlinear Hall effect does not expected for this material, which we confirm as negligibly small second-harmonic transverse Hall voltage response to the longitudinal ac electric current. As the main experimental result, we demonstrate the unsaturated third-harmonic Hall response in NiTe${}_2$, which well corresponds to the theoretically predicted third-order nonlinear Hall effect in Dirac semimetals. We also demonstrate, that the third harmonic signal does not depend on the external magnetic field, in contrast to the field-depended first-order and second-order Hall effects.