heterostructures*

Twisted bilayers of graphene (tBLG) offer a new platform where interlayer Coulomb interactions can be tailored conveniently. The formation of extremely flat bands at certain ‘magic’ angles, where the Coulomb energy exceeds the bandwidth, has led to the observation of correlated insulating states, superconductivity and other exotic states such as Chern insulators, orbital ferromagnets, and nematic phases. The dielectric environment of tBLG plays an important role in controlling electronic correlations within the flat bands. In this work, we have explored various facets of many-body correlations using a combination of magneto-transport and thermoelectric measurements in tBLG coupled to a layer of tungsten diselenide (WSe₂). We observe states near half-integer band fillings 0.5 and ±3.5 at near-zero magnetic fields and a symmetry-broken Chern insulator at -0.5 emerging at high magnetic fields. The results can be explained using band structure calculations within a translational symmetry-broken supercell with twice the area of the original tBLG moiré cell, suggestive of a spin or charge density wave ground state. Furthermore, below half-filling, we report anomalous Hall effect with a giant coercive field, accompanied by a series of Lifshitz transitions that are highly tunable with carrier density and magnetic field. We infer that the observed valley ordering is favored by a Stoner-like instability, aided by van Hove singularities in the malleable bands. Overall, our results suggest that transition metal dichalcogenide- dielectrics can be a promising pathway to further understand and explore the nature of correlated phases in tBLG systems.