As the circles move across one another, watch out for patterns. These patterns are created by two sets obliquely offset from one another and are known as moire (pronounced mwara-AY). Moire patterns are optical illusions that create neat simulations for movement. These moire patterns, which are essentially optical illusions, can be used to create atomic-scale physics. When one sheet of atoms is slightly offset from the other, it can result in some interesting and important physics.

University of Utah mathematicians have discovered that they can create a variety of composite materials using moire patterns. This is created by rotating and stretching each lattice relative. The resulting moire patterns can have a variety of physical and electrical properties. This depends on whether they are regular repeating or not. Communications Physics publishes their findings.

Kenneth Golden, distinguished professor in mathematics, states that the mathematics and physics behind these twisted lattices can be applied to many material properties. The underlying theory is also applicable to materials with a wide range of lengths, from nanometers up to kilometers. This shows how broad our potential technological applications are.

With a twist

Before we can arrive at these new discoveries, we need to trace the history of two key concepts: aperiodic geometries and twistronics.

Aperiodic geometry refers to patterns that aren't repeated. Penrose's tiling pattern is a good example of this. You won't find the right part of the design if you just draw a rectangle around it and then start moving it in any direction without rotating it.

Girih tiles used in Islamic architecture have aperiodic patterns that were created over 1000 years ago. In the 1980s, Dan Shechtman, a materials scientist, discovered a crystal that had an aperiodic, atomic structure. This breakthrough in crystallography was a result of Shechtman's discovery of an atomic structure that is not regularly repeated. Shechtman won the Nobel Prize in Chemistry 2011.

Now, let's move on to twistronics. This field also has a Nobel in it's lineage. For discovering graphene in 2010, Andre Geim, Konstantin Novoselov were awarded the Nobel Prize in Physics. This material is made up of one layer of carbon atoms in an atomic lattice that looks almost like chicken wire. Graphene has many interesting properties. However, physicists discovered that if you stack two layers, and then turn one, the resulting graphene becomes a superconductor. This material is also extraordinarily strong. This area of research focuses on the electronic properties of twisted bilayergraphene. It is known as "twistronics."

Composites in two phases

Golden and his coworkers came up with something new in the new study. It works like twistronics but instead of having two layers of atoms the moire patterns created from interfering lattices control how two different materials components (such as a conductor or a poor one) are organized geometrically into a composite. The new material is called a "twisted bilayer compound" because one lattice is stretched and/or twisted relative to the other. They discovered that moire patterns can have surprising properties when they study the mathematics of such materials.

"As the scale and twist angles vary, these patterns give myriad microgeometries. Very small changes in these parameters can cause very large changes to the material properties," said Ben Murphy, coauthor and adjunct professor of mathematics.

For example, twisting one lattice only two degrees can cause moire patterns to change from being regularly repeated to not-repeating. This can make them appear random and chaotic, which is similar to the on/off behavior of semiconductors in computer chips. The material can also be used as an insulator to prevent current from flowing through the patterns. This is similar to rubber that covers the handle of a hand tool and helps eliminate electric shock.

Researchers were reminded of another Nobel-winning discovery, the Anderson localization transition in quantum conductors. This discovery won the 1977 Nobel Prize in Physics. It explains how electrons can travel freely through materials (a conductor), or get trapped or localized in a material (an insulator). It uses the mathematics of interference and wave scattering. Golden points out that Anderson's quantum wave equations don't apply to these twisted bilayer compounds, so it must be another factor that creates the conductor/insulator effect. Golden states, "We observed a geometry-driven localization transformation that has nothing do with wave scattering and interference effects. This is an unexpected and surprising discovery."

These new materials have such a wide range of electromagnetic properties that engineers might use it to tune its properties and select the visible frequencies of light. The frequencies that the material will block and the colors it will allow for are determined by the material's properties.

"Moreover, our mathematical framework can tune other properties of these material, such as magnetic and diffusive as well as optical, and electrical," Elena Cherkaev, professor of mathematics, study co-author, says. "This points to the possibility of similar behavior for acoustic or other mechanical analogues."