Moiré superlattices have become an emergent solid-state platform for simulating quantum lattice models. However, in a single moiré device, Hamiltonian parameters like the lattice constant, hopping, and interaction terms can hardly be manipulated, limiting the controllability and accessibility of a moiré quantum simulator. Here, by combining angle-resolved photoemission spectroscopy and theoretical analysis, we demonstrate that high-order moiré patterns in graphene-monolayered xenon/krypton heterostructures can simulate a honeycomb model in the mesoscale, with in situ tunable Hamiltonian parameters. The length scale of the simulated lattice constant can be tuned by annealing processes, which in situ adjusts intervalley interaction and hopping parameters in the simulated honeycomb lattice. The sign of the lattice constant can be switched by choosing a xenon or krypton monolayer deposited on graphene, which controls the sublattice degree of freedom and valley arrangement of Dirac fermions. In this letter, we establish a path for experimentally simulating the honeycomb model with tunable parameters by high-order moiré patterns.

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• Electronic structure
• First-principles calculations
• Quantum simulation
• Graphene
• Twisted heterostructures
• Angle-resolved photoemission spectroscopy