Programming the third-order nonlinear Hall effect by dimensionality and electric field

Active control of nonlinear electrical responses in materials is crucial for developing novel mixing, rectification and sensing circuits. Here, we report full-range programming of both the sign and magnitude of the third-order nonlinear Hall effect (NLHE) in the topological semimetal TaIrTe4 using all-electrical means. We show that this third-order NLHE is governed by a quantum coherence length. By fabricating a series of devices with various thicknesses for the TaIrTe4 layer and using an DC electric field control, we map a clear operational phase diagram. In the three-dimensional competing state, the third-order NLHE reverses its sign at a critical temperature (~ 23 K), and this reversal temperature can be tuned by the electric field. In the quantum coherence length limited state, the effect is locked to a single sign. This work provides a proof of principle for creating reconfigurable nonlinear topological electronic devices through synergistic geometric and electrical design.