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.
Moiré superlattice period: L ≈ a / (2·sin(θ/2))
a ≈ 0.246 nm (graphene lattice constant), θ = twist angle
θ ≈ 1.05–1.1° → "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 and lattice 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, generating a visible moiré pattern; near 1.1° for bilayer graphene it opens the "magic angle" flat-band regime.
- 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.