  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 characterization 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 unique patterns among the probed atomic groups for the first time. 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.
