Berry curvature dipole senses topological transition in a moire superlattice

Topological aspects of the electron wave function-including the Berry curvature and Chern number-play a crucial role in determining the physical properties of materials. Although the Berry curvature and its effects in materials have been studied(1,)(2), detecting changes in the Chern number can be challenging, particularly changes in the valley Chern type. In this regard, twisted double bilayer graphene(3-7) has emerged as a promising platform to gain electrical control over the Berry curvature hotspots(8) and the valley Chern numbers of topological flat bands(9,10). In addition, strain-induced breaking of the threefold rotation symmetry leads to a non-zero first moment of Berry curvature (called the Berry curvature dipole)(11). Here we show that a sign change in the Berry curvature dipole detects topological transitions in the bands. In twisted double bilayer graphene, the perpendicular electric field simultaneously tunes the valley Chern number and Berry curvature dipole, providing a tunable system to probe the topological transitions. Furthermore, we find hysteresis in the transport response that is caused by switching of the electric polarization. This holds promise for next-generation Berry-curvature-based memory devices. Our technique can be emulated in three-dimensional topological systems to probe topological transitions governed by parameters such as pressure or anisotropic strain.