A glass of ice water offers a familiar example of two phases existing at the same time. The same substance can appear as both liquid water and solid ice. In certain quantum materials, different phases can also coexist, although the underlying behavior is far more complex.
MIT physicists have now uncovered new details about how two distinct forms of electron organization can emerge within the same quantum material.
The findings, published in Nature Physics, could improve scientists’ understanding of materials that display superconductivity, magnetism, and other electronic phases. Learning how these phases arise and interact could eventually help researchers gain greater control over electronic properties and develop more powerful quantum devices.
“People believe the cornerstone of replacing silicon lies in quantum materials that have multiple coexisting phases,” says co-author Alfred Zong PhD ’20, who co-led the study as an MIT graduate student and is now an assistant professor at Stanford University. “Our experiment provides a very neat way to study these multiple phases.”
An Atomic Checkerboard of Electrons
The researchers, led by Nuh Gedik, the Donner Professor of Physics at MIT, investigated erbium tritelluride, a rare-earth material with unusual electronic behavior.
Under ordinary conditions, electrons are distributed relatively evenly throughout erbium tritelluride. When the material is cooled to specific temperatures, however, the electrons begin organizing themselves into a wave-shaped arrangement known as a “charge density wave” (CDW) phase.
Cooling the material even further produces a second wave pattern running perpendicular to the first. Together, the two electronic phases form something resembling an atomic-scale checkerboard.
Gedik and his colleagues were able to separate the behavior of these two phases and observe how each one developed. The first phase appeared gradually across the material, somewhat like liquid water steadily becoming vapor. This matches the conventional picture of how many electronic phase transitions take place.
The second phase behaved very differently. Rather than appearing smoothly throughout the material, it began in isolated regions that expanded outward, resembling the way ice crystals begin forming in liquid water.
“The mechanism responsible for the emergence of this second phase has long been debated, and our approach provides a powerful new way to uncover the hidden physics behind phase transitions in quantum materials,” Gedik says.
The study’s other MIT co-authors are first authors Yifan Su PhD ’24 and Bai-Qing Lv, a former postdoc; Dongsung Choi SM ’17, PhD ’24; and former postdocs Doron Azoury and Masataka Mogi; along with collaborators from multiple other institutions.
How Charge Density Waves Form
A charge density wave develops when electric charges such as electrons spontaneously organize into a repeating wave pattern. Regions corresponding to the crests contain more electrons, while the troughs contain fewer. In some materials, this coordinated state appears only at extremely low temperatures.
Physicists have studied charge density waves for decades. More recently, researchers have found them in materials that also support more complicated forms of collective electron behavior, including magnetism and superconductivity, in which electrons pair together and move through a material without friction.
“Just like superconductivty, charge density waves are a collective phenomena where electrons move together in certain ways,” explains lead author Yifan Su. “The power of CDWs is that they are a much simpler form of matter compared to superconductivity. They offer a playground for fundamental understanding.”
The researchers wanted to study a material in which two CDW phases exist at the same time. Understanding how the two waves appear and coexist could provide clues about the more complicated phase transitions involved in superconductivity and other unusual electronic states.
“One of the biggest questions in physics is why some materials host multiple phases while others do not. And when multiple phases do exist, how do they interact? Do they reinforce one another, compete, or coexist independently?” Gedik says. “This is like a case study for us to understand much more complicated materials.”
Using Lasers to Disturb Quantum Order
Scientists already knew that erbium tritelluride can support two different charge density waves. The rare-earth material can be produced in the laboratory as atomically thin sheets, allowing researchers to probe its unusual quantum-scale properties.
Earlier experiments showed that the first charge density wave appears when erbium tritelluride is cooled to -8 degrees Celsius. This “dominant” wave extends through the material in one direction.
When the temperature drops further to -113 degrees Celsius, a second “subdominant” charge density wave appears at a right angle to the first. The two patterns together create the checkerboard arrangement of coexisting electronic phases.
For the new study, Gedik’s team wanted to determine exactly how each phase forms.
The researchers obtained small, atomically thin samples of erbium tritelluride created by collaborators at Stanford. In Gedik’s laboratory, they cooled the samples to roughly -230 degrees Celsius, cold enough for both charge density waves to exist simultaneously in the checkerboard pattern.
They then disrupted or destroyed that electronic pattern and watched to see how the two waves returned.
The experiment relied on two carefully timed laser pulses.
“This is how we ‘shake’ and then ‘listen’ to the system,” Gedik says.
The first laser pulse served as the “shake,” breaking apart the electronic checkerboard. By changing the pulse intensity, the researchers could control how strongly they disturbed the charge density waves.
A second pulse containing high-energy photons then knocked electrons out of the material. The researchers applied this pulse at different intervals after the first one and measured the energy and momentum of the expelled electrons. Those measurements provided a series of snapshots showing how the electronic phases recovered over time.
“We see the destroying of these phases, and then if we wait long enough, they come back,” Gedik explains. “And depending on how you hit them, the two phases respond differently.”
Two Very Different Ways to Rebuild
The dominant charge density wave returned gradually and evenly, regardless of how strongly the researchers had initially disrupted the material.
That smooth recovery is considered a textbook “second-order” phase transition. It resembles the gradual way a magnet loses its magnetism as its temperature rises.
The second charge density wave produced the bigger surprise.
Instead of returning uniformly, the subdominant phase began forming in scattered pockets. Those regions then expanded through the material, much like ice crystals growing through liquid water.
This behavior corresponds to a less common “first-order” transition and was not what the researchers expected. The observations allowed the team to identify the long-debated mechanism responsible for the emergence of the subdominant CDW phase.
The findings may have implications well beyond erbium tritelluride. More complicated quantum materials can contain several electronic phases simultaneously, and scientists suspect that the way those phases interact may be responsible for some of their most unusual properties.
“In systems that are much more complex, like high-temperature superconductors, you see there are multiple phases — magnetism, superconductivity, charge density waves, and they all exist together,” Gedik says. “One of the theories is that, the way they interact with each other is key for their exotic properties. The lessons we learn here can be applied to much more complex materials.”
The research was supported by the U.S. Department of Energy, the U.S. National Science Foundation, and the Gordon and Betty Moore Foundation’s EPiQS Initiative grant.
