moire pattern
/ mwah-RAY PAT-ern /
You have probably seen this on a video call: when someone wears a finely striped shirt, the camera shows shimmering wavy bands that are not really on the shirt at all. Look through two layers of a thin curtain and you see something similar — large rippling shapes that neither layer has on its own. That ghostly large-scale pattern is a moire pattern.
A moire pattern appears whenever two regular grids are overlaid with a slight mismatch — either a small difference in spacing or a small twist between them. Where the two grids' lines happen to fall on top of each other you get bright spots; where they fall into each other's gaps you get dark spots; and these regions of agreement and disagreement repeat over a much larger distance than the original grids. So a tiny mismatch produces a pattern far bigger than either grid alone, magnifying the small difference into something easy to see.
Moire patterns matter far beyond optical curiosities: when two atomic crystal lattices are stacked with a slight twist, the resulting moire pattern acts as a giant artificial lattice that reshapes how electrons move, and this is the heart of the recent revolution in twisted two-dimensional materials. The honest caveat is that the pattern is not a physical object you could pick up — it is an interference effect, a pattern of where two underlying grids agree, with no new atoms or lines added anywhere.
Lay two combs of slightly different tooth spacing one over the other and slide them: dark bands sweep along, racing far faster and spanning far wider than any single tooth. The same trick, played with two atomic lattices, builds the superlattice behind twisted bilayer graphene.
Two slightly mismatched combs reveal sweeping dark bands far larger than their teeth — a moire pattern.
The smaller the mismatch or twist, the larger the moire pattern — so in twisted crystals a smaller twist angle gives a bigger moire cell, which is exactly why such tiny angle changes can have outsized effects on the electrons.