Engineering Hubbard models in gated two-dimensional moiré systems

Layered van der Waals materials have become a versatile platform for exploring correlated electronic behavior from superconductivity and topological order to correlated insulating states. These systems not only hold promise for quantum technologies but also provide a controllable setting to test fundamental theories of interacting electrons. The Hubbard model serves as a cornerstone for understanding correlated quantum matter, yet it remains analytically intractable in most regimes. Moiré materials now offer an experimental pathway to emulate such models with tunable parameters.

We show that a two-dimensional electron gas subject to a moiré potential and dual metallic gates can be tuned to realize the physics of the square-lattice Hubbard model. Using density functional theory with an exchange-correlation functional derived from quantum Monte Carlo data, we map the evolution of its phases as a function of gate separation and moiré potential depth. The system reproduces hallmark Hubbard model features, including antiferromagnetism and stripe order at fractional filling. Through downfolding to an effective lattice Hamiltonian, we establish quantitative agreement with Hubbard parameters, offering a concrete route to engineer and probe correlated electron phases in moiré materials.