New, highly tunable composite materials—with a twist
Note the patterns created as the circles move over each other. Those patterns, created by two sets of lines shifted relative to each other, are called moire (pronounced mwar-AY) effects. Like optical illusions, moiré patterns create neat simulations of movement. But at the atomic scale, when a sheet of atoms arranged in a lattice is slightly offset from another sheet, these moiré patterns can create some exciting and important physics with interesting and unusual electronic properties.
Mathematicians at the University of Utah have discovered that they can design a series of composite materials based on moiré patterns created by rotating and stretching one grid relative to another. Their electrical and other physical properties can change – sometimes quite abruptly, depending on whether the resulting moiré patterns repeat regularly or not. Their findings have been published in Communication physics†
The math and physics of these twisted lattices applies to a wide variety of material properties, says Kenneth Golden, distinguished professor of mathematics. “The underlying theory also applies to materials at a wide range of length scales, from nanometers to kilometers, demonstrating how broad the scope is for potential technological applications of our findings.”
with a twist
Before we arrive at these new findings, we need to chart the history of two important concepts: aperiodic geometry and twistronics.
Aperiodic geometry means patterns that do not repeat. An example is the Penrose tiling pattern of diamonds. If you draw a box around part of the pattern and start sliding it in any direction without rotating it, you will never find a part of the pattern that matches it.
Aperiodic patterns designed over 1000 years ago appeared in Girih tiles used in Islamic architecture. More recently, in the early 1980s, materials scientist Dan Shechtman discovered a crystal with an aperiodic atomic structure. This revolutionized crystallography, as the classical definition of a crystal includes only regularly repeating atomic patterns, and earned Shechtman the 2011 Nobel Prize in Chemistry.
Okay, now to twistronics, a field that also has a Nobel Prize. In 2010, Andre Geim and Konstantin Novoselov won the Nobel Prize in Physics for discovering graphene, a material made of a single layer of carbon atoms in a lattice that looks like chicken wire. Graphene itself has its own set of interesting properties, but in recent years physicists have found that when you stack two layers of graphene on top of each other and twist one around a bit, the resulting material becomes a superconductor that is also extremely strong. This area of research of the electronic properties of twisted bilayer graphene is called ‘twistronics’.
In the new study, Golden and his colleagues imagined something different. It’s like twistronics, but instead of two layers of atoms, the moiré patterns formed by interfering lattices determine how two different material components, such as a good conductor and a bad one, are arranged geometrically in a composite material. They call the new material a “twisted double-layer composite” because one of the grids is twisted and/or stretched relative to the other. When they examined the mathematics of such a material, they found that moiré patterns yielded some surprising properties.
“Because the twist angle and scale parameters vary, these patterns yield numerous microgeometries, with very small changes in the parameters causing very large changes in the material properties,” said Ben Murphy, co-author of the paper and adjunct assistant professor of mathematics. .
For example, if you rotate one grid just two degrees, the moiré patterns can go from regularly repeating to non-repeating — and even appear randomly disordered, even though all patterns are non-random. If the pattern is ordered and periodic, the material can conduct electric current very well or not at all, with on/off behavior similar to semiconductors used in computer chips. But for the aperiodic, disordered patterns, the material may act as a current-crushing insulator, “similar to the rubber on the handle of a tool that helps eliminate electric shock,” said David Morison, lead author of the study who recently completed his Ph.D. in physics from the University of Utah under Golden’s supervision.
This kind of abrupt transition from electrical conductor to insulator reminded the researchers of yet another Nobel Prize-winning discovery: the Anderson localization transition for quantum conductors. That discovery, which won the Nobel Prize in Physics in 1977, explains how an electron can move freely through a material (a conductor), or become trapped or localized (an insulator), using the mathematics of wave scattering and interference. But Golden says the quantum wave equations Anderson used don’t work at the scale of these twisted bilayer composites, so something else must be going on to create this conductor/insulator effect. “We observe a geometry-driven localization transition that has nothing to do with wave scattering or interference effects, which is a surprising and unexpected discovery,” says Golden.
The electromagnetic properties of these new materials vary so widely with only small changes in the angle of rotation that engineers could one day use that variation to fine-tune a material’s properties and, for example, adjust the visible frequencies of light (also called colors). select the material that will pass and the frequencies it will block.
“In addition, our mathematical framework applies to tuning other properties of these materials, such as magnetic, diffuse and thermal, as well as optical and electrical,” said professor of mathematics and co-author of the study Elena Cherkaev, “pointing to the possibility of similar behavior in acoustic and other mechanical analogs.”
Researchers improve charge density waves through moiré engineering in twisted hterostructures
Order to disorder in quasiperiodic composites, Communication physics (2022). DOI: 10.1038/s42005-022-00898-z
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