Real space characterization of nonlinear hall effect in confined directions

The nonlinear Hall effect (NLHE) is a phenomenon which could produce a transverse Hall voltage in a time-reversal-invariant material. Here, we report the real space characterizations of NLHE evaluated through quantum transport in TaIrTe₄ nanoribbon without the explicit Berry curvature dipole (BCD) information. We first characterize the NLHE in both transverse confined directions in global-level measurement. The impact of quantum confinement in NLHE is evaluated by adjusting the width of nanoribbons. Then, the probing area is trimmed to the atomic scale to evaluate the local texture, where we discover its patterns differ among the probed neighboring atomic groups. The analysis of charge distribution reveals the connections between NLHE’s local patterns and its non-centrosymmetric nature, rendering nearly an order of Hall voltage enhancement through probe positioning. Our work paves the way to expand the range of NLHE study and unveil its physics in more versatile material systems.