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A Moiré pattern is a large-scale modulation produced by superposing similar periodic structures. Two identical two-dimensional lattices rotated by a small angle $\theta$ have geometric period $L=a/[2\sin (\theta /2)]\simeq a/|\theta |$ in the usual matching geometry. In layered crystals this modulation can act as an electronic superlattice; the actual bands additionally depend on interlayer coupling and orbital structure.

The Moiré pattern sets a superlattice periodFor the stipulated scalar one-dimensional model, right- and left-moving states have $E(k)=\hslash v|k|$. The $n$th Bragg crossing satisfies $E(k)=E(k-nG)$ and hence $k=nG/2$. The Bragg gap ladder for a linear dispersion therefore has centresThis is the spacing of successive possible Bragg gaps. The corresponding atomic-lattice scale is $hv/(2a)\simeq 8.27\mathrm{eV}$, fifty times larger.

Shifting a linear branch by one full reciprocal period $G$ instead gives $\hslash vG\simeq 0.331\mathrm{eV}$, twice the consecutive Bragg-threshold spacing; the first zone boundary is at $G/2$. These scales should not be confused with the gap width, which depends on the weak potential's Fourier coefficients. The geometry alone does not guarantee equally wide or even observable gaps at every threshold, nor an exactly periodic full spectrum. The estimate neglects graphene's additional pseudospin selection rules and interlayer correlations, as required by the scalar-chain approximation.

A superlattice is a spatial periodic structure with a repeat length larger than an underlying atomic lattice period. Its additional reciprocal lattice vectors fold electronic bands into a smaller Brillouin zone, and allowed couplings can open small gaps at the folded crossings. The gap sizes depend on potential Fourier components and symmetry, not on the geometric period alone.