Moiré superlattices make use of the phenomenon the moiré pattern, in which the wave interference of two similar patterns create new, often mesmerizing and undulating patterns.
Wigner Crystals’ Behavior Charted and Compared with Theory, Providing New Tool for Studying Possible Electronics Components
To design the next generation of smaller, more powerful electronic devices, scientists will need to understand better how the materials act at the smallest scales. In moiré superlattices, scientists lay sheets of identical or similar materials just an atom thick atop each other. These materials may promise finely tuned electronic behaviors at tiny distances. But their behavior doesn’t always match with existing theory. A team from Florida State University used PSC’s NSF-funded Bridges-2 to explore how a type of matter on a triangular moiré superlattice behaves, suggesting how scientists can improve their theory and supplying a new tool for materials engineers to use in designing devices.
WHY IT’S IMPORTANT
Apple’s M3 Ultra computer chip, which powers the latest iPhones and iMacs, contains 184 billion transistors. The tiny “metal lines” that carry electrons through the device can be as close together as 24 nanometers — about a millionth of an inch. At that scale, the weird rules of quantum mechanics, by which electrons are waves and can jump across otherwise “solid” barriers, take over.
As our electronics get smaller, it gets harder to determine how they’ll behave. Knocking together components and seeing what happens isn’t economical or effective. Instead, you first need to figure out how materials work at the most basic level.
Such basic science doesn’t always create new devices. But it gives the designers the rules they need to figure new devices out.
One set of materials that scientists would like to understand better are moiré superlattices. These materials offer enhanced tunability, because it may be possible to design them to control movement of electrons across their structure — what computer scientists call “gate voltages.” One particular moiré system has two sheets of slightly mismatched materials called transition metal dichalcogenides, each only an atom thick.
The mismatch pattern creates a large moiré unit cell. These larger structures in the material reduce the energy scales of the layers by as much as a thousand times. This allows scientists to study behaviors at energy scales that would simply not be accessible for conventional materials.
“We are interested in modeling electronic phases of matter, which are distinct from the structural phases we know from everyday life — you know, solid, liquid, gas … But the electrons, which you do not see with your bare eyes, have a world of their own and can transform from one phase to another … A lot of our work is motivated by the ability to predict and to understand: What do electrons do in different situations?”
— Hitesh Changlani, FSU and Maglab
Aman Kumar, a Dirac postdoctoral fellow at the National High Magnetic Field Laboratory (Maglab), working with Florida State University’s Hitesh Changlani and Cyprian Lewandowski, wanted to better understand a kind of triangular moiré superlattice formed by the electrons in a Wigner crystal. A crucial tool in their investigation was PSC’s flagship Bridges-2 supercomputer.
HOW PSC HELPED
In quantum mechanics, electrons don’t behave as particles. Instead, they are waves, typically spreading out and delocalizing. Everyday metals, such as copper and aluminum, conduct electricity because the electrons, despite having the same negative charge, are spread out farther apart in a kind of soup, and so don’t repel each other as strongly.
A moiré superlattice greatly suppresses that kind of electron delocalization. At certain densities, electrons suddenly “see” each other’s charge, and freeze in place. Instead of being a conductor like a metal, they are now an insulator, blocking electrical current. This behavior could allow engineers to tune the crystal by altering the density through changing the gate voltage, or by varying twist angles.
When scientists built real Wigner crystals in the lab, though, the frozen electrons melted at a lower temperature than classical theory had predicted. Also, two forms of Wigner crystals, with triangular versus honeycomb arrangements of atoms, showed different melting points, when the theory said they should be the same. The quantum rules were making themselves felt.
To understand how the system worked, Kumar would need to simulate the electrons in the Wigner crystal using the rules of quantum statistical mechanics. Each theoretical model would require dealing with matrices that have about 100 million dimensions, using hundreds of different starting points and then averaging them. To avoid slowdowns in the calculations as the computer went back and forth from data storage to its computing nodes, the system would need to store a considerable amount of memory in its RAM.
“When you are in the low temperature phase, you have this nice, ordered pattern of electrons. That is the Wigner crystal. When you are in the high-temperature phase, the crystal has melted. So, to understand this melting transition, and to locate where this transition was happening and compare it with experiments, we need to restart this algorithm many, many times.”
— Aman Kumar, FSU
Bridges-2 proved ideal for the work, with regular nodes containing either 256 or 512 gigabytes of memory. That’s four to eight times as much RAM as in a hot laptop computer. And Bridges-2 has 504 of these nodes.
The simulations helped explain the melting behavior of the triangular and honeycomb Wigner crystals. The simulations also showed how and when the quantum behavior started showing up. Importantly, the results suggest that Wigner crystals naturally exist at a point very close to the metal-insulator transition. That’s the point at which the electrons switch between carrying electrical currents and blocking them. This means that small changes in the crystals can produce large changes in behavior, which could prove useful to materials engineers. The team reported their results in the journal npj Quantum Materials in August 2025.
The team is currently exploring the effects of two factors for controlling the Wigner crystals’ behavior — the temperature and the electron kinetic energy/bandwidth. Just as importantly, Kumar’s work has provided a new tool for the group to continue studying Wigner crystals in moiré superlattices, at other electron densities where patterns such as stripes have been realized. The computer models make predictions on how these materials will behave, which lab scientists can use to study them in the real world.