Berry curvature dipole senses topological transition in a moiré superlattice

Topological aspects of electron wavefunction play a crucial role in determining the physical properties materials. Berry curvature and Chern number are used to define topological structure electronic bands. While its effects materials have been studied, detecting changes invariant, number, is challenging. In this regard, twisted double bilayer graphene (TDBG) has emerged as promising platform gain electrical control over hotspots valley numbers flat addition, strain induced breaking three-fold rotation (C3) symmetry TDBG, leads non-zero first moment called dipole (BCD), which can be sensed using nonlinear Hall (NLH) effect. We reveal, that BCD detects transitions bands sign. perpendicular electric field tunes simultaneously allowing us tunable system probe physics transitions. Furthermore, we find hysteresis longitudinal NLH responses with attributed switching polarization moir\'e systems. Such hysteretic response holds promise for next-generation curvature-based memory devices. Probing transitions, show, emulated other 3D