Hofstadter states and re-entrant charge order in a semiconductor moiré lattice

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/MoSe₂ heterobilayer 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.