Physicists at the University of Illinois Urbana-Champaign’s Grainger College of Engineering have uncovered groundbreaking evidence of an unusual form of superconducting behavior hidden within the heavy-fermion material uranium ditelluride. Their rigorous experiments reveal that Cooper pairs—the foundational paired electrons that make traditional and unconventional superconductivity possible—can spontaneously organize themselves into uneven, periodic patterns even after the bulk material has transitioned out of its main superconducting state.
These elusive patterns are known to physicists as pair density waves, or PDWs. First theorized by researchers about two decades ago, previous scientific studies had managed to observe them coexisting alongside standard superconductivity in a handful of other metallic systems. However, this new research, which has been published in the Proceedings of the National Academy of Sciences, pushes the boundaries of condensed matter physics much further. It provides the first direct, compelling evidence that pair density waves in uranium ditelluride can survive within the material’s ordinary phase long after traditional bulk superconductivity has completely disappeared.
"Pair density waves are the Cheshire Cat’s grin of superconductivity," said Eduardo Fradkin, an Illinois Grainger Engineering physics professor and a co-lead of the research project. "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."
The breakthrough was made possible by a combination of material synthesis and advanced measurement techniques. "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 project’s other 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
To understand the magnitude of this discovery, it helps to examine the foundational mechanics of superconductivity. Superconductivity is a remarkable quantum phenomenon that occurs when certain metals are cooled below a specific critical temperature, allowing them to carry electrical current with absolute zero resistance. In this deeply ordered state, the material’s free electrons settle into a collective, low-energy quantum state.
This creates a fundamental physical challenge. Electrons belong to a broad class of subatomic particles known as fermions. One of the core rules of quantum mechanics—the Pauli exclusion principle—strictly prevents identical fermions from occupying the exact same quantum state. Superconductivity manages to bypass this roadblock through a much more complex cooperative process involving pairs of electrons.
In 1957, legendary Illinois physicists John Bardeen, Leon Cooper, and Robert Schrieffer formulated a microscopic theory explaining this behavior, which famously became known as BCS theory. According to their model, individual electrons first become correlated through interactions with the metal’s underlying atomic lattice. One electron then dynamically pairs with another, forming what is known as a Cooper pair.
Unlike individual electrons, which act as fermions, these coupled Cooper pairs behave collectively as bosons. Because bosons are not subject to the same quantum restrictions as fermions, many of them can comfortably occupy the same quantum state without experiencing mutual repulsion. Once paired up, they condense together into a unified macroscopic quantum state, giving rise to zero-resistance superconductivity.
BCS theory successfully explained virtually all known superconducting behavior for nearly three decades, until scientists discovered a new class of "unconventional" superconductors in 1986. These exotic materials stubbornly refuse to fit the foundational assumptions and predictions of BCS theory, even though their electrons still successfully form Cooper pairs and undergo condensation. Unraveling the exact microscopic mechanisms governing how unconventional superconductors operate remains one of the most active and intensely debated areas of modern physics research.
The Mystery of Pair Density Waves
Unconventional superconductors frequently play host to other complex electronic phases at temperatures sitting below the primary superconducting critical temperature. One well-documented example is charge density waves, or CDWs, in which a fraction of the material’s electrons spontaneously organize into a repeating, nonuniform spatial pattern. The resulting state features a periodic variation in electronic charge density, with certain microscopic regions containing a higher concentration of electric charge while neighboring regions contain less.
In 2007, Eduardo Fradkin and his academic collaborators proposed the existence of yet another exotic phase, which they dubbed a pair density wave. In a standard, textbook superconductor, Cooper pairs are distributed uniformly and evenly throughout the material. However, the researchers hypothesized that under the right conditions, these pairs might instead arrange themselves into repeating, spatially modulated patterns.
Their theoretical model put forward a particularly unusual prediction: pair density waves could theoretically survive at temperatures above the material’s critical temperature. If true, this meant that Cooper pairs could successfully form even when the host material had not officially entered its macroscopic superconducting phase.
" extérieureWe were out on a limb when we first suggested it," Fradkin recalled, reflecting on the early days of the hypothesis. "It’s a very peculiar state, and, although there have been experimental hints over the years, there has been no direct confirmation of the phase’s existence."
Julian May-Mann, a former Illinois Grainger Engineering graduate student who contributed to the study’s theoretical analysis, noted the immense experimental hurdles involved. "PDWs are tricky to analyze in real materials, because they behave like conventional superconductors in some experiments, and like CDWs in others," he explained. "Confirming the existence of a PDW requires both high-quality experimental data as well as careful theoretical analysis."
Why Uranium Ditelluride Stands Out
Until relatively recently, specifically 2019, uranium ditelluride was widely regarded by the scientific community as an ordinary, unexceptional metal. That perspective shifted dramatically when researchers discovered that it undergoes a transition into a superconducting phase when cooled below 2 kelvins.
Further experimental investigations led physicists to suspect that uranium ditelluride might belong to a rare and fascinating class of materials known as triplet-pair superconductors. Unlike the conventional singlet electron pairs described by standard BCS theory—where the paired electron spins point in opposite directions—triplet electron pairs possess parallel spins and net magnetic moments.
To date, the only definitively confirmed example of a triplet-pair macroscopic "super-phase" is superfluid helium-3. That complex quantum system was extensively studied by the late Illinois physicist Anthony Leggett, whose pioneering work earned him a Nobel Prize in Physics.
"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 focused attention of Vidya Madhavan’s experimental research group. Utilizing advanced scanning tunneling microscopy, the team successfully identified charge density waves within the material. However, something about the behavior of these waves defied standard expectations. Crucially, external magnetic fields were able to 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 pointed out. "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 rigorously investigate the hypothesis of pair density waves, Madhavan’s team first required significantly cleaner, higher-purity samples of uranium ditelluride. PDWs are notoriously delicate electronic states that demand highly regular, defect-free crystal lattices in order to manifest clearly.
Collaborating researchers supplied superior samples produced via a newly refined molten flux growth method. The research team then examined these pristine crystals using a sophisticated vector magnetic field scanning tunneling microscope. This specialized apparatus enables scientists to observe precisely how a material’s electronic surface responds to magnetic fields applied simultaneously from multiple, independent directions.
"We couldn’t see pair density waves in our earlier data because of material impurities that obscured our data," Madhavan explained. "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."
Zhen Zhu, an Illinois Grainger Engineering physics postdoctoral research associate who spearheaded the physical experiments, emphasized the critical role played by the new instrumentation. "A key advantage of our experiment was the newly developed vector-magnet equipment, which provides an unusually large magnetic-field range along multiple directions," Zhu said. "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
Detailed measurements of the charge density waves revealed distinct modes that shifted dynamically with both temperature and magnetic field strength in the exact manner theoretically predicted for pair density waves. Furthermore, external magnetic effects readily destroyed these modes, aligning perfectly with the team’s theoretical framework.
The most dramatic and revealing result emerged when the researchers elevated the temperature of the samples. Remarkably, certain observed modes continued to persist even after the material was heated past its critical temperature, causing the bulk superconducting phase to vanish entirely.
"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 noted. "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 readily acknowledge an important experimental limitation: scanning tunneling microscopy imaging exclusively measures electronic phenomena occurring at a material’s exposed surface. Consequently, the experiment does not directly visualize what is transpiring deep within the bulk interior of the uranium ditelluride crystal. Even so, the research team is confident that these surface findings provide an exceptionally strong diagnostic clue that could unlock new pathways 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 added. "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."
Additional contributions to this research were made by Yudi Huang, Kaiming Liu, Zheyu Wu, Shanta Saha, Johnpierre Paglione, Alexander Eaton, Andrej Cabala, and Michal Vališka. Financial support for the project was provided by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division.
