As the circles move across each other, watch for the pattern created. There are two sets of lines that are offset from each other. A neat simulation of movement is created by the moiré patterns. At the atomic scale, when one sheet of atoms is slightly offset from another, these patterns can create some exciting and important physics.
A group of mathematicians at the University of Utah have found that they can design a range of materials from the same pattern. Depending on whether the pattern is regularly repeating or non-repeating, their electrical and other physical properties can change. Their findings can be found in Communications physics.
Kenneth Golden says that the mathematics and physics of twisted lattices apply to a wide variety of material properties. The scope of our findings is demonstrated by the fact that materials on a large range of length scales, from nanometers to kilometers, are held in the underlying theory.
There is a twist.
We will need to chart the history of aperiodic geometry and twistronics before we get to these new findings.
A pattern that doesn't repeat is called aperiodic geometry. The Penrose pattern is rhombuses. You won't find a part of the pattern that matches it if you draw a box around it and slide it in any direction.
Over 1000 years ago, aperiodic patterns were used in tilings. Dan Shechtman discovered a crystal with an aperiodic atomic structure in the early 1980's. The classic definition of a crystal includes only regular repeating atomic patterns, which earned Shechtman the 2011 Nobel Prize in chemistry.
There is a field called twistronics that has a prize in it's genealogy. The discovery of a material that's made of a single layer of carbon atoms in a lattice that looks like chicken wire was the subject of a 2010 physics prize. Physicists have found that when you stack two layers of Graphene together, they become a superconductor that is very strong. "Twists" is a field of study of the electronic properties of bilayers.
The two-phase material is made of two phases.
Golden and his colleagues came up with a new idea. It's like twistronics, but instead of two layers of atoms, the patterns formed from interfering lattices determine how two different material components, such as a good conductor and a bad one, are arranged. Since one of the lattices is stretched relative to the other, the new material is called a twisted bilayer. They found some surprising properties in the math of the material.
Ben Murphy is a co-author of the paper and an assistant professor of mathematics.
The moiré patterns can go from regular repeating to non-repeating if one lattice is twisted just two degrees. The material can conduct electrical current very well or not at all if it is ordered and periodic. The material can be a current-squashing insulator, like the rubber on the handle of a tool that helps to eliminate electrical shock, according to the lead author of the study.
The researchers of the Anderson Localization transition for quantum conductors were reminded of this sudden transition from electrical conductor to insulator. The physics of wave scattering and interference explains how an electron can move through a conductor or an insturment. Golden says that the quantum wave equations Anderson used don't work on the scale of these twisted bilayer composites, so there must be something else going on. Golden says that there is a geometry-driven transition that has nothing to do with wave scattering or interference effects.
Engineers may one day use the variation in the twist angle to tune a material's properties, for example, the visible frequencies of light.
"Our mathematical framework applies to tuning other properties of these materials, such as magnetic, diffusive and thermal, as well as optical and electrical," says professor of mathematics and study co-author Elena Cherkaev.
More information: Order to disorder in quasiperiodic composites, Communications Physics (2022). DOI: 10.1038/s42005-022-00898-z Journal information: Communications Physics
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