Physicists at the University of Illinois Urbana-Champaign’s Grainger College of Engineering have uncovered evidence of an unusual form of superconducting behavior in uranium ditelluride. Their experiments show that Cooper pairs, the paired electrons that make superconductivity possible, can arrange themselves into uneven patterns even when the material is no longer in its main superconducting state.
These patterns are called pair density waves (PDWs). Scientists first predicted them about 20 years ago, and previous studies have observed them alongside superconductivity in other metals. The new research, published in the Proceedings of the National Academy of Sciences, goes further. It provides the first direct evidence that PDWs in uranium ditelluride can remain in the material’s “ordinary” phase after superconductivity has disappeared.
“Pair density waves are the Cheshire Cat’s grin of superconductivity,” said Eduardo Fradkin, an Illinois Grainger Engineering physics professor and a project co-lead. “They are the vestige that remains once the phase itself has disappeared. In conventional superconductors, Cooper pairs form when the full phase transition occurs, but, in this system, their observation in PDWs above the transition point shows that they are formed beforehand in a different state.”
“Thanks to new methods for growing higher-quality samples, we were able to observe spectral signatures that respond to temperature and magnetic fields exactly as pair density waves should,” said Vidya Madhavan, an Illinois Grainger Engineering physics professor and the other project co-lead. “We even showed that the modes persist above the temperature at which superconductivity disappears, a telltale theoretical prediction that has not been convincingly observed before now.”
How Unconventional Superconductors Behave
Superconductivity occurs when a metal can carry electricity with zero resistance after being cooled below a critical temperature. In this state, the material’s free electrons settle into a low-energy quantum state.
That creates a fundamental challenge. Electrons belong to a group of particles called fermions, and quantum mechanics prevents fermions from gathering in the same state. Superconductivity gets around this restriction through a more complicated process involving pairs of electrons.
In 1957, Illinois physicists John Bardeen, Leon Cooper and Robert Schrieffer explained this behavior with what became known as BCS theory. According to their model, electrons first become correlated through interactions with the metal’s underlying lattice. One electron then pairs with another to create a Cooper pair.
Unlike individual electrons, Cooper pairs behave as bosons. That means many of them can occupy the same quantum state without the repulsion that applies to individual fermions. Once paired, they can condense together into a superconducting state.
BCS theory successfully explained known superconducting behavior until scientists discovered “unconventional” superconductors in 1986. These materials do not fit the assumptions behind BCS theory, even though their electrons still form Cooper pairs and condense. Understanding exactly how unconventional superconductors work remains an active area of physics research.
The Mystery of Pair Density Waves
Unconventional superconductors often host other electronic phases at temperatures below the superconducting critical temperature. One example is charge density waves (CDWs), in which some electrons form a repeating, nonuniform pattern. The result is a periodic variation in charge, with some regions containing more electric charge and others containing less.
In 2007, Fradkin and his colleagues proposed another possible phase known as a pair density wave. Cooper pairs are normally distributed uniformly throughout a superconductor, but the researchers suggested that the pairs might also arrange themselves into repeating patterns.
Their theory made a particularly unusual prediction. Pair density waves could potentially survive above the critical temperature, which would mean Cooper pairs could form even when a material had not entered its superconducting phase.
“We were out on a limb when we first suggested it,” Fradkin said. “It’s a very peculiar state, and, although there have been experimental hints, there has been no direct confirmation of the phase’s existence.”
“PDWs are tricky to analyze in real materials, because they behave like conventional superconductors in some experiments, and like CDWs in other,” said Julian May-Mann, a former Illinois Grainger Engineering graduate student who worked on the study’s theoretical analysis. “Confirming the existence of a PDW requires both high-quality experimental data as well as careful theoretical analysis.
Why Uranium Ditelluride Stands Out
Until 2019, uranium ditelluride was generally considered an ordinary metal. That changed when researchers discovered that it enters a superconducting phase below 2 kelvins.
Further investigation led physicists to suspect that uranium ditelluride could be a rare triplet-pair superconductor. Unlike the electron pairs described by BCS theory, triplet electron pairs possess magnetic moments.
The only confirmed example of a triplet-pair ‘super-phase’ is superfluid helium-3. The system was extensively studied by the late Illinois physicist Anthony Leggett, who received the Nobel Prize for this work.
“Triplet-pair superconductors with properties analogous to superfluid helium-3 are conjectured to exist, and there are several superconductors believed to be such instances,” Fradkin said. “I would not say that the question is completely settled, but the consensus is that uranium ditelluride is a triplet-pair superconductor.”
Uranium ditelluride eventually drew the attention of Madhavan’s experimental research group. Using scanning tunneling microscopy, the team identified CDWs in the material. But something about those waves did not behave as expected. Magnetic fields could destroy them.
“A charge density wave is just a collective electronic state that is modulated in space, so there is no reason for them to respond to magnetic fields, let alone be destroyed by them,” Madhavan said. “We took our data to Professor Fradkin and his students, and we predicted that this could happen if there is also a pair density wave in the system. There aren’t many possible explanations for something like this, and pair density waves are the best one I can think of.”
Better Crystals Reveal the Hidden State
To investigate the possibility of pair density waves, Madhavan’s team first needed much cleaner samples of uranium ditelluride. PDWs are extremely delicate and require highly regular crystals to form.
Collaborators supplied higher quality samples produced with a new molten flux growth method. The researchers then examined them using a vector magnetic field scanning tunneling microscope (STM), which allows scientists to study how a material’s surface responds to magnetic fields applied from different directions.
“We couldn’t see pair density waves in our earlier data because of material impurities that obscured our data,” Madhavan said. “It would have been like trying to spot a light in a cloud of fog. But we succeeded with the better samples because of our new vector magnetic field equipment. The latter was especially important because uranium ditelluride is anisotropic, so we needed the capability to examine the crystals from many directions.”
“A key advantage of our experiment was the newly developed vector-magnet equipment, which provides an unusually large magnetic-field range along multiple directions,” said Zhen Zhu, an Illinois Grainger Engineering physics postdoctoral research associate who carried out the experiments. “This capability is particularly well suited to uranium ditelluride, whose superconducting upper critical field is strongly anisotropic. By systematically varying both the magnitude and direction of the field, together with temperature, we could track how these modes evolved and build confidence that the behavior we observed was intrinsic.”
Cooper Pairs Persist After Superconductivity Vanishes
The measurements of the CDWs revealed modes that changed with temperature and magnetic field in the way expected for PDWs. Magnetic effects could destroy them, just as the pair density wave explanation predicted.
The most striking result came when the researchers raised the temperature. Some modes continued to exist even after the material passed its critical temperature and the main superconducting phase disappeared.
“There are foundational principles in condensed matter physics that constrain how different phases can appear and disappear when one changes the temperature or applies a magnetic field,” May-Mann said. “Any explanation of the experimental data that only relies on a CDW is at odds with these principles. The PDW-based explanation, on the other hand, provides a satisfactory and consistent explanation.”
The researchers note an important limitation. STM imaging only measures effects at a material’s surface, so the experiment does not directly reveal what is happening throughout the interior of uranium ditelluride. Even so, the team believes the findings offer a strong clue and could open new directions for studying unconventional superconductivity.
“It is possible for the interior of a material to behave differently than the surface, but these experimental results still give us a very strong hint at what’s happening inside,” Fradkin said.
“As an experimentalist, one of the most satisfying things is when several independent measurements begin to tell the same story,” Zhu said. “Here, the temperature and magnetic-field dependence, together with the improved sample quality, all came together to reveal a remarkably consistent picture of the pair density wave state.”
Yudi Huang, Kaiming Liu, Zheyu Wu, Shanta Saha, Johnpierre Paglione, Alexander Eaton, Andrej Cabala and Michal Vališka also contributed to this work.
Support was provided by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division.
