Moiré pattern

A moiré pattern arises when two repeating patterns—such as line gratings, grids or crystal lattices—are superposed but do not align exactly. Their local mismatch changes gradually across the overlap, producing broad light-and-dark bands or a larger-scale lattice. For two parallel line gratings with slightly different pitches, the spacing of the broad beat fringes grows as their pitches become more alike. For two identical line patterns rotated by a small angle, the moiré spacing likewise increases as the angle decreases. The observed structure is a consequence of the superposition and relative geometry of the originals.

Because the broad fringes respond sensitively to small changes in position, angle or spacing, moiré patterns can make otherwise tiny displacements easier to observe. Grating-based moiré methods are used in dimensional measurement and in mapping deformation or strain. Similar effects appear when fine meshes, printed screens or digital displays overlap. In imaging, the pattern is often an unwanted artifact: a camera sensor samples a repeating subject on its own pixel grid, and the interaction can produce visible bands or false textures.

In crystals made by stacking two atomically thin layers, a small twist or lattice mismatch creates a periodic moiré superlattice. In twisted bilayer graphene, the moiré periodicity and interlayer coupling depend on the relative rotation. Theoretical work showed that at certain small twist angles the electronic bands can become unusually flat. Experiments reported superconductivity and correlated insulating states in devices near a so-called magic angle of about 1.1 degrees. These results helped establish moiré materials as a way to tune electronic properties through layer geometry. They apply to particular carefully prepared systems; a moiré pattern alone does not guarantee superconductivity.

The same geometric principle links everyday interference-like fringes, precision measurement and engineered quantum materials. In a macroscopic grating, the broad pattern is useful as a sensitive readout of alignment. In a crystal, the long-wavelength modulation can reshape the effective electronic environment experienced by electrons. Interpreting a moiré image or material therefore requires knowing the underlying patterns and their relative orientation, rather than treating the fringes as an independent material feature.