Harnessing Intrinsic Nonlinear Hall Effect in PT-Symmetric Antiferromagnetic Topological Insulators

The intrinsic nonlinear Hall effect (NLHE) has emerged as a powerful probe of band geometry and symmetry breaking beyond linear response. Unlike the anomalous Hall effect, which requires time-reversal symmetry breaking, the intrinsic NLHE occurs when both time-reversal and inversion symmetries are broken—even in the absence of mobile carriers. Using a density-matrix formalism, we derive a unified expression for the intrinsic nonlinear Hall conductivity that separates Fermi-surface and Fermi-sea contributions. Remarkably, we find that the Fermi-sea term remains finite in insulating states, giving rise to a robust nonlinear Hall response even when the linear Hall effect is symmetry-forbidden. Applying this framework to a PT-symmetric antiferromagnetic topological insulator, we show that the NLHE directly encodes the underlying Néel order and can thus serve as an all-electrical detection mechanism for insulating AFM memory devices. These results reveal how quantum geometry enables dissipationless nonlinear transport in magnetic insulators and provide a route toward readout of antiferromagnetic order in topological materials.