Boundary-Bulk Interplay in Nonlinear Topological Transport

Nonlinear transport provides a powerful probe of the quantum geometry of electronic wavefunctions in topological materials. While nonlinear responses from bulk quantum geometry and band topology are well understood, the role of boundary modes remains largely unexplored. In this work, we demonstrate boundary-bulk interplay in nonlinear transport, including second-harmonic Hall and nonreciprocal longitudinal responses, in molecular beam epitaxy-grown magnetic topological insulator heterostructures. We find that the nonlinear transport is maximized when the sample is tuned slightly away from well-quantized quantum anomalous Hall and axion insulator states. The sign and amplitude of the nonlinear responses depend on electrode configuration, magnetic order, and carrier type. Supported by symmetry analysis and nonlinear Landauer-Büttiker formalism, our findings demonstrate that nonlinear transport is governed by the interplay between boundary and bulk states. Our work highlights the critical role of electrodes in nonlinear transport and establishes boundary modes as a key origin of the giant nonlinear response in nearly bulk-insulating topological materials.