Two-dimensional materials are only a few atoms thick yet hold great promise for the electronics of tomorrow. Because they are so thin, they can be piled in strange, twisted configurations that yield new physical behaviors not known to exist previously. One of the most slippery of these is a type of atomic vibration called a phason—a special type of motion long believed in by scientists but never actually seen.
Now, for the first time, that has changed.
Imaging the Invisible in Atomic Vibrations
Using a novel imaging technique known as electron ptychography, scientists have directly imaged phasons in a twisted 2D material called tungsten diselenide. Their research reveals how those tiny vibrations vary with atomic arrangement and provides the most accurate images of individual atoms ever recorded.
(left) atoms present in the 2D material. (right) photos of single atoms. (CREDIT: The Grainger College of Engineering)
They are only a special case of a broader category of moiré phonons, the result of when two layers of 2D material are shifted slightly one from the other. That fold between the two creates a moiré superlattice—a larger periodic structure that gives rise to unique thermal and electronic behavior. Phasons are an extremely soft, low-frequency variety of these phonons.
Even though phonons and phasons are not seen, their effect is widespread. Heat is atomic vibration in itself, and an understanding of such patterns is required if one expects to have any control over heat transfer in electronics. Greater control could imply materials that cool faster or suck heat off sensitive parts.
You can’t just get rid of phasons; that’s the blessing and curse,” said Pinshane Huang, a professor of materials science and engineering at the University of Illinois at Urbana-Champaign and lead author of the paper. “They’ve always been hiding in plain sight, changing the properties of 2D moiré materials.”
A Microscopic Leap in Clarity
Phasons had mystified scientists for decades. They were thought to belong in theoretical models only, but no one had concrete proof. Not until Huang teamed up with Yichao Zhang, a postdoctoral researcher of nanoscale heat conduction. Their task: to freeze the blur of atomic movement created by heat.
Pinshane Huang. (CREDIT: Brian Stauffer)
What our primary goal was, was to see heat when looking at an atom,” Huang explained. “What this does is get so fantastic spatial resolution that vibrations of the atoms have something to do with how fuzzy the atoms appear,” she said. “These are tiny movements, and we can basically look at one atom at a time and see its heat-related motion.”.
To do this, the team utilized electron ptychography, a new imaging method with a resolution of less than 15 picometers. That is about one-thousandth the width of an individual atom. It allowed the team to see the width, shape, and movement of atoms in twisted bilayer tungsten diselenide, or WSe₂.
“Back when I started out, we figured the highest resolution you could get was maybe a little bit less than an angstrom,” Huang said. “But once ptychography arrived on the scene, we were starting to see resolution numbers as low as 0.2 angstroms,” she continued. “That put us thinking, ‘Well, heat gets atoms jigged around about 0.05 angstroms,’ she said. “Now that we can actually see heat, it shows what a giant jump in resolution can do for what microscopes can do,” she continued.
A Closer Look at Twisted Layers
Twisted structures are important because they alter the local atomic environment in strong and unexpected manners. When one layer is twisted against another in bilayer materials such as WSe₂, there is a mismatch in the grids of atoms. That mismatch creates new areas—some with atoms close together and others not so close.
Illustration of experimental measurement of thermal vibrations in a single atom. (CREDIT: Yichao Zhang, et al.)
When researchers mapped these helical regions, they found more vibrations in some areas. Vibrations were especially strong around solitons, where solitons are borders between different stacking modes. AA-stacked regions, in which atoms lie atop each other, also showed more intense vibrations.
By integrating electron ptychography with lattice dynamics and molecular dynamics simulations, the scientists made a robust conclusion. Phasons were discovered by them as the main culprit behind thermal vibration in low-angle twisted bilayers. This tells us that the moiré pattern is not just an illusion—it plays a pivotal role in determining how heat traverses through the material. These findings provide new doors to investigate and even control heat in 2D materials at the atomic level.
To a New Generation of Devices
Phasons are tiny, but their potential effect could be huge. Controlling the skill of sensing and studying these vibrations could change the way electronics are designed in the future. “One potential application of this technique is creating materials that are better heat conductors,” said Zhang. “We can look at one atom and find a defect that keeps the material from cooling more efficiently,” he said.
This could result in better means of atomic-level thermal control,” he added. “To watch individual atoms and see how they react to heat will tell us some very important things,” he said.
Experimental and MD comparison of single W atom sizes. (CREDIT: Yichao Zhang, et al.)
Twisted 2D materials are already being researched for use in transistors, sensors, and quantum computing hardware. Adding heat behavior to that research means engineers can create entire devices at the atomic level. Such devices would be able to be made smaller, faster, and much more efficient than today’s electronics.
Perhaps most exciting is the manner in which this finding reconciles theory with direct observation. Phasons were previously hypothetical, known by equations and models alone. Now, they are observable in real time.
Using equipment like electron ptychography, even the slightest motion of the atoms can be watched and measured. Science no longer needs to speculate about what atoms do—it’s watching them in plain sight, one vibration at a time.
Research findings are available online in the journal Science.
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