You are probably familiar with moiré patterns, large-scale disturbance patterns known for mathematics, physics, and art. They are built by covering one light pattern with clear spaces on top of another similar pattern. When they are turned or removed, a disturbing way appears.
Moiré patterns have proven to be especially useful for 2D objects; single-layer objects are lattices that comprise a single layer of atoms. Graphene, a single layer of atoms arranged in a two-dimensional honeycomb lattice nanostructure, is one of the best-known 2D materials. If you take two stacks of graphene twisted with a magic angle, all kinds of robust structures such as superconductivity and ferromagnetism can appear.
View created patterns as circles move by themselves. Those patterns, created by two sets of lines removed from each other, are called moiré effects (war-AY). Like visual perceptions, moiré patterns make a beautiful imitation of movement. But on the atomic scale, when one sheet of atoms arranged in a lattice moves slightly away from another sheet, these moiré patterns can create exciting and essential physics with interesting and unusual electronic features.
Mathematicians at the University of Utah have found that they can design a range of composites from moiré patterns created by rotating and extending one lattice relative to another. Their electrical and other physical properties may change — sometimes suddenly, depending on whether the resulting moiré patterns are repeated or not. Their findings were published in Communication Physics.
The statistics and physics of these twisted lattices work on various materials, says Kenneth Golden, a prominent professor of mathematics. “Basic theory also captures objects on a large scale in length, from nanometers to kilometers, which indicates the wide range of potential technological uses of our findings.”