Catalogue · stack
Stack two layers
Lay one sheet on another and their lattices beat against each other in a moiré pattern. Pick two of 47 materials and a twist angle to see how far apart the lattices are, how large the moiré is, and which small supercells fit both layers – the cells a calculation would start from.
Supercells that fit both layers
A calculation needs a cell that repeats in both layers at once. These are the smallest: a supercell of the top layer, spanned by m·a₁ + n·a₂ and the same turned by 60° (90° on a square lattice), laid on one of the bottom layer whose sides are as long, the top one stretched or squeezed by the strain given. Choose one to set its twist.
| Twist | Top cell (m, n) | Bottom cell (m, n) | Top layer strained | Atoms |
|---|
No supercell up to 14 cells along each side fits within this strain. Allow more.
Or begin with
Lattice constants are those of the models on each material’s page, measured on bulk crystals, mostly at room temperature; CuInP₂S₆, CrI₃, α-RuCl₃, FePS₃ are stored in rectangular cells that are hexagonal to within 0.1%, and count as hexagonal. The moiré period follows from the two shortest lattice vectors, λ = a₁a₂ / √(a₁² + a₂² − 2a₁a₂ cos θ), which for two identical layers is a / 2 sin(θ/2); the moiré’s turn is measured from the bottom layer and, the pattern repeating every 60° (90° on a square lattice), given up to 30° (45°). Real layers relax and pick up strain, and close to alignment a change of 0.1% in either lattice moves a long period a good deal, so read it as a guide. Rectangular lattices – phosphorene, SnSe, WTe₂ and others – are left out, because their moiré stretches differently along the two directions.