Each 2D material is a single- or few-atom-thick crystal held together within the plane by strong covalent bonds, while separate layers stack via weak van der Waals forces — no chemical bonds between layers, so any two 2D crystals can be combined like atomic Lego. Overlaying two hexagonal lattices at a small twist angle θ produces a moiré superlattice: a much larger periodic pattern of bright (locally aligned, "AA-stacked") and dark (locally offset, "AB-stacked") regions.
Moiré superlattice wavelength: λ = a / (2·sin(θ/2))
a = lattice constant of the selected material, θ = twist angle
θ ≈ 1.05–1.1° (graphene-on-graphene) → "magic angle" → flat bands → correlated insulator / superconductivity
Band gap by material (monolayer):
graphene Eg ≈ 0 eV (zero-gap semimetal, Dirac fermions)
h-BN Eg ≈ 6.0 eV (wide-gap insulator)
MoS₂ Eg ≈ 1.8 eV direct (monolayer) → indirect, smaller gap once stacked
MXene Eg ≈ 0 eV (metallic Ti₃C₂Tₓ conduction)
- Material — switches the atomic composition, lattice constant and sublattice coloring, changing which formulas above apply.
- Stacked layers — adds monolayers above the base one; MoS₂'s direct band gap becomes indirect once a second layer hybridizes with the first.
- Twist angle — rotates each added layer relative to the one below by θ, L (its layer index); the canvas overlays the resulting lattices with additive brightness so the moiré fringes appear exactly like a real dark-field TEM moiré image.
- Interlayer spacing — the van der Waals gap between sheets; smaller spacing means stronger interlayer electronic coupling.
Real devices stack exactly this way: graphene/h-BN/graphene sandwiches give a clean conducting channel next to a perfect dielectric, and MoS₂-based transistors exploit the direct-gap monolayer for LEDs and photodetectors. This 2D top-down view is the natural companion to the 3D stacking sim: a flat material is best read as a plan-view interference pattern, not a camera angle on a 3D stack.