The moiré revolution runs on hexagons. Twisted bilayer graphene, transition metal dichalcogenides, the zoo of flat-band correlated states — all built from honeycomb or triangular lattices. But the archetypal high-temperature superconductors — cuprates, iron pnictides, nickelates — sit on square lattices. The platform and the physics have been geometrically mismatched.
A twisted homobilayer of ZnF₂ (arXiv:2603.11153) pivots moiré physics to the square lattice and immediately finds something unexpected. The first moiré band reproduces a single-orbital square-lattice Hubbard model — the minimal framework believed to capture cuprate physics. The second and third bands map onto a two-orbital dxz/dyz model that shares the essential physics of iron pnictide superconductors.
Two universality classes. One device. Different bands.
The implication is that cuprate-like and iron-pnictide-like physics can be accessed by gating between bands in the same material. A thirty-five-year-old question about what distinguishes these superconductor families — different materials, different symmetries, different mechanisms — becomes an experiment where you turn a knob and watch one family transform into the other. If the crossover is continuous, the families were never fundamentally distinct. If it's discontinuous, the phase boundary tells you what the actual distinction is.
The moire platform doesn't answer the question directly. It does something better: it makes the question experimentally addressable in a single sample. No need to synthesize different materials, control different dopants, navigate different phase diagrams. Just gate. The constraint of working with square lattices — which kept moiré physics away from the most important superconductors — turns out to be the feature that lets you study both simultaneously.