The interplay of field-tunable strongly correlated states in a multi-orbital moiré system

The interplay of charge, spin, lattice and orbital degrees of freedom leads to a variety of emergent phenomena in strongly correlated systems. In transition-metal-dichalcogenide-based moiré heterostructures, recent observations of correlated phases can be described by triangular-lattice single-orbital Hubbard models based on moiré bands derived from the Brillouin-zone corners—the so-called K valleys. Richer phase diagrams described by multi-orbital Hubbard models are possible with hexagonal lattices that host moiré bands at the zone centre—called Γ valleys—or an additional layer degree of freedom. Here we report the tunable interaction between strongly correlated hole states hosted by Γ- and K-derived bands in a heterostructure of monolayer MoSe 2 and bilayer 2H WSe 2 . We characterize the behaviour of exciton–polarons to distinguish the layer and valley degrees of freedom. The Γ band gives rise to a charge-transfer insulator described by a two-orbital Hubbard model. An out-of-plane electric field re-orders the Γ- and K-derived bands and drives the redistribution of carriers to the layer-polarized K orbital, generating Wigner crystals and Mott insulating states. Finally, we obtain degeneracy of the Γ and K orbitals at the Fermi level and observe interacting correlated states with phase transitions dependent on the doping density. Our results establish a platform to investigate multi-orbital Hubbard model Hamiltonians. Heterostructures of transition metal dichalcogenides are known to simulate the triangular-lattice Hubbard model. Now, by combining a monolayer and bilayer of different materials, this idea is extended to multi-orbital Hubbard models.