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Moiré superlattices formed from transition metal dichalcogenides support a variety of quantum electronic phases that are highly tunable using applied electromagnetic fields. While the valley degree of freedom affects optoelectronic properties in the constituent transition metal dichalcogenides, it has yet to be fully explored in moiré systems. Here we establish twisted double-bilayer WSe2as an experimental platform to study electronic correlations within Γ-valley moiré bands. Through local and global electronic compressibility measurements, we identify charge-ordered phases at multiple integer and fractional moiré fillings. By measuring the magnetic field dependence of their energy gaps and the chemical potential upon doping, we reveal spin-polarized ground states with spin-polaron quasiparticle excitations. In addition, an applied displacement field induces a metal–insulator transition driven by tuning between Γ- and K-valley moiré bands. Our results demonstrate control over the spin and valley character of the correlated ground and excited states in this system.

The emergence of moiré materials with flat bands provides a platform to systematically investigate and precisely control the correlated electronic phases. Here we report on a rich phase diagram of interpenetrating Hofstadter states—also called Chern insulators—and electron solids in a twisted WSe2/MoSe2heterobilayer using local electronic compressibility measurements. We show that this reflects the presence of both flat and dispersive moiré bands whose relative energies, and therefore occupations, are tuned by the density and magnetic field. At low density, the competition between moiré bands leads to a transition from the commensurate arrangements of singlets at doubly occupied sites to triplet configurations at high fields. Hofstadter states are generally favoured at high density as dispersive bands are populated, but are suppressed by an intervening region of re-entrant charge-ordered states in which holes originating from multiple bands cooperatively crystallize. Our results reveal the key microscopic ingredients that favour distinct correlated ground states in semiconductor moiré systems, and they demonstrate an emergent lattice model system in which both interactions and band dispersion can be experimentally controlled.