A universal design principle for switchable control of the second-order nonlinear Hall effect.

Manipulating the nonlinear Hall effect (NLHE) through non-volatile approach is of great significance for device applications, yet effective gating control remains elusive. In this Letter, using first-principles calculations and symmetry analysis, we propose a universal design principle for gate-field control of the NLHE in bilayer systems. Using bilayer SnSe and SnTe, the well-known ferroelectric and thermoelectric materials, as examples, it reveals that the inherent hidden polarization can activate a layer-locked hidden Berry curvature dipole (BCD) under an applied gate field, thereby inducing a giant nonlinear Hall current. The hidden polarization locked to BCD in a gate field, experiences a pseudospin Zeeman field as a spin in magnetic field. Therefore, reversing the direction of the gate-field can switch the preferred pseudospin orientation, enabling the switchable second-order NLHE. The gate field strengthens the spin-orbit coupling, leading to energy-band splitting that further enhances the BCD contribution. This mechanism does not require intrinsic magnetism and provides a binary ON/OFF switching control method, greatly expanding the application potential of layered systems in nonlinear Hall transport. Our findings not only demonstrate the universal design principle of the switchable second-order NLHE but also can be extended to other gate-field-controllable nonlinear transport and nonlinear optics.