Observation of Berry curvature fluctuations from incipient polar order in an oxide interface
Diagnosing hidden local orders at buried interfaces remains a central challenge in the design and characterization of quantum materials. Second-order electrical responses, such as the nonlinear Hall effect, probe inversion-symmetry-breaking terms invisible to linear transport, offering a direct window into these nanoscale environments via the quantum geometry of Bloch electrons. Here, we utilize $\text{KTaO}_3$, a complex oxide driven by strong tantalum $5d$ spin-orbit coupling and interfacial inversion symmetry breaking, to demonstrate that second-harmonic resistivities exhibit large, reproducible mesoscopic fluctuations. Remarkably, these fluctuations persist in macroscopically large ($200\,\mu\text{m}$) devices and are ubiquitous across all studied surface orientations, even where macroscopic conductivity strictly adheres to underlying crystal symmetries. We propose that these robust, magnetic-field-driven interference patterns arise from local structural symmetry breaking, driven by incipient ferroelectric polarization pinned to the interfacial impurity landscape. This defect-pinned polar mechanism is firmly supported by the signal's suppression above $10\text{ K}$ due to phase decoherence, and a complete loss of mesoscopic memory upon thermal cycling above $40\text{ K}$. By linking quantum geometry to dynamic lattice ordering, our findings establish nonlinear mesoscopic transport as a powerful new characterization tool, capable of revealing local polar tendencies and hidden structural orders in complex materials that remain fundamentally invisible to conventional probes.