Tunable atomically enhanced moir\'e Berry curvatures in twisted triple bilayer graphene

We report a twisted triple bilayer graphene platform consisting of three units of Bernal bilayer graphene consecutively twisted at 1.49{\deg} and 1.68{\deg}. We demonstrate the atomic reconstruction between the two competing moir\'e superlattices strongly enhances the Berry curvature of each moir\'e band insulator state, characterized by measured strong nonlocal valley Hall effect that sensitively depends on the inter-moir\'e competition strength, tunable by manipulating the out-of-plane carrier distribution. Our study sheds light on the microscopic mechanism of atomic and electronic reconstruction in twisted multilayer systems, by systematically investigating transport signatures of moir\'e Berry curvature and its enhancement from moir\'e-of-moir\'e lattice reconstruction. We show that the reconstructed electronic band can be versatilely tuned by electrostatics, providing an approach toward engineering the band structure and its topology for a quantum material platform with designer electrical and optical properties.