Berry curvature dipole senses topological transition in a moiré superlattice*

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