Electric field control of third-order nonlinear Hall effect

The third-order nonlinear Hall effect (NLHE) serves as a sensitive probe of energy band geometric property, providing a new paradigm for revealing the Berry curvature distribution and topological response of quantum materials. In the Weyl semimetal TaIrTe4, we report for the first time that the sign of the third-order NLHE reverses with decreasing temperature. Through scaling law analysis, we think that the third-order NLHE at high (T > 23 K) and low (T < 23 K) temperatures is dominated by Berry-connection polarizability (BCP) and impurity scattering, respectively. The third-order NLHE response strength can be effectively modulated by an additional applied in-plane constant electric field. At the high temperature region, the BCP reduction induced by the electric field leads to a decrease in the third-order NLHE response strength, while at the low temperature region, the electric field cause both BCP and impurity scattering effects to weaken, resulting in a more significant modulation of the third-order NLHE response strength. At 4 K and an electric field strength of 0.3 kV/cm, the modulated relative response strength could reach up to 65.3%. This work provides a new means to explore the third-order NLHE and a valuable reference for the development of novel electronic devices.