Physicists watch a material’s electrons assemble, and reassemble, into coexisting phases

A tall glass of ice water isn’t just a thirst quencher; it’s also an everyday example of coexisting phases. Water’s molecular makeup can exist simultaneously in both a liquid and solid phase. And as it turns out, this phase duality can exist in more exotic, quantum materials, and in ways that are far more complicated to tease apart.

A new study by MIT physicists sheds light on how two different phases of electron behavior can emerge and coexist in the same quantum material.

Their results, reported today in the journal Nature Physics, can help to explain how some materials host superconductivity, magnetism, and other electronic phases. Untangling such phases, and understanding how they emerge, will help engineers control electronic behavior and design high-performance 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.”

The team, led by Nuh Gedik, the Donner Professor of Physics at MIT, studied the rare-earth material erbium tritelluride. As with most materials, erbium tritelluride’s electrons are normally scattered uniformly throughout the material. But when cooled to certain temperatures, the electrons suddenly organize into a wave-like pattern, which physicists term a “charge density wave” (CDW) phase. When cooled even further, electrons coordinate again as a second wavy phase that criss-crosses the first. The effect is of an atomic checkerboard of co-existing electron phases.

Now, Gedik and his colleagues have teased apart erbium tritelluride’s phases and observed how each phase emerges. They found that one phase forms gradually, similar to how liquid water transitions uniformly into vapor. This is the classic, textbook way in which electronic phase transitions are thought to occur.

But the second phase came about in an entirely new and unexpected way: Instead of emerging gradually, the electrons organized first in pockets that eventually expanded, similar to how liquid water crystallizes into ice.

“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.

A clear view

A charge density wave is made up of charges, such as electrons, that spontaneously organize as a wave. The wave’s crests hold the highest density of electrons, and the lowest are found in the troughs. In some materials, electrons transition into this strange coordinated phase at super-cold temperatures.

Scientists have observed charge density waves for decades, and most recently in materials that also host other, more complicated forms of electron coordination, such as various forms of magnetism, and superconductivity, in which electrons pair up and flow 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.”

Su and the team looked to get a clear view of charge density waves in a material that hosts two CDW phases simultaneously. How these waves emerge and coexist in a single material could shed light on how superconductivity and other more complicated phase transitions occur.

“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.”

Shake, then listen

Scientists have observed two different charge density waves in erbium tritelluride — a rare-earth material that can be synthesized in the lab, in atomically thin sheets that can then be probed for unique, quantum-scale properties.

In previous experiments, physicists have found that when erbium tritelluride is cooled down to -8 degrees Celsius, the first of two charge density waves forms among the material’s electrons. This “dominant” wave stretches across the material in one direction. When the material is further cooled to -113 degrees Celsius, a second, “subdominant” charge density wave emerges, perpendicular to the first, creating a checkerboard of coexisting electronic phases.

In their new study, Gedik and his colleagues sought to tease out how each phase emerges in erbium tritelluride. The team obtained small, atomically thin samples of the material, which were synthesized by collaborators at Stanford. In Gedik’s lab, the researchers then cooled the samples down to about -230 degrees Celsius — temperatures at which the material should host both charge density waves, in a simultaneous, checkerboard pattern. They then either destroyed or weakened the checkerboard, and watched how both types of waves reemerged.

To do so, they exposed each cooled sample to a one-two punch of laser pulses.

“This is how we ‘shake’ and then ‘listen’ to the system,” Gedik says.

The first pulse was the “shake” that dissolved the checkerboard. The researchers could control the intensity of this kick to vary the degree to which the waves were disturbed. They then delivered a second laser pulse, of high-energy photons, to kick out electrons from the material. This second pulse was sent in at various times after the first pulse. The researchers then measured the energy and momentum of the kicked-out electrons, to get snapshots of how the material’s electronic phases recovered.

“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.”

From their experiments, the team found that the first, dominant phase of charge density waves reemerges gradually and uniformly, no matter how hard the material was initially “kicked.” This smooth restoration is a textbook, “second-order” phase transition, similar to a magnet gradually losing its magnetism as it is heated.

What was more surprising was how the second wave pattern reemerged. This subdominant phase reformed more like water into ice. The electrons reassembled the wave in isolated pockets that spread, like crystals of ice. This more rare, “first-order” transition was not expected. The team’s study captured the the long-debated mechanism underlying the emergence of the subdominant CDW phase.

“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.”

This work 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.