Physicists at the University of Illinois Urbana-Champaign’s Grainger College of Engineering have uncovered groundbreaking evidence of an unusual form of superconducting behavior in the heavy-fermion material uranium ditelluride. Their rigorous experiments reveal that Cooper pairs—the coupled electrons that make zero-resistance superconductivity possible—can arrange themselves into uneven, periodic patterns even when the bulk material is no longer in its primary superconducting state.
These spatial patterns are known as pair density waves, or PDWs. Theoretical physicists first predicted their existence approximately two decades ago, and subsequent studies have occasionally observed them coexisting alongside superconductivity in various other metals. However, the new research, recently published in the Proceedings of the National Academy of Sciences, pushes the boundaries of condensed matter physics significantly further. It provides the first direct empirical evidence that PDWs in uranium ditelluride can survive within the material’s ordinary phase long after traditional superconductivity has completely vanished.
"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 advanced material synthesis and cutting-edge microscopy. "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," explained 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 is a remarkable quantum phenomenon that occurs when certain metals are cooled below a critical temperature, allowing them to carry electrical current with absolute zero resistance. In this ultra-low-energy state, the material’s free electrons settle into a collective quantum state.
This creates a fundamental physical challenge. Electrons belong to a class of subatomic particles called fermions. The foundational laws of quantum mechanics—specifically the Pauli exclusion principle—strictly prevent identical fermions from gathering in the exact same quantum state. Superconductivity cleverly bypasses this restrictive rule through a more intricate cooperation process involving pairs of electrons.
Back in 1957, legendary Illinois physicists John Bardeen, Leon Cooper, and Robert Schrieffer formulated an explanation for this behavior, which became universally known as BCS theory. According to their landmark model, electrons become correlated through dynamic interactions with the metal’s underlying atomic lattice. One electron then binds with another to create what is formally termed a Cooper pair.
Unlike individual electrons, Cooper pairs behave as bosons rather than fermions. This distinction is critical because bosons are not bound by the Pauli exclusion principle; multiple bosons can comfortably occupy the exact same quantum state without the mutual repulsion that governs individual fermions. Once paired up, these bosons can condense collectively into a macroscopic superconducting state.
While BCS theory successfully explained standard superconducting phenomena for decades, everything shifted in 1986 with the discovery of "unconventional" superconductors. These complex materials stubbornly refuse to fit the foundational assumptions of BCS theory, even though their electrons still manage to form Cooper pairs and condense. Decoding the precise mechanisms behind unconventional superconductivity remains one of the most active and challenging frontiers in modern physics research.
The Mystery of Pair Density Waves
Unconventional superconductors frequently host a variety of secondary electronic phases at temperatures sitting below the primary superconducting critical temperature. A prominent example is charge density waves, or CDWs, in which a subset of electrons spontaneously self-organizes into a repeating, nonuniform spatial pattern. The result is a periodic modulation of electric charge throughout the material, creating alternating microscopic regions containing higher and lower concentrations of electric charge.
In 2007, Professor Fradkin and his academic collaborators proposed the existence of an even more elusive phase: the pair density wave. In a typical superconductor, Cooper pairs are distributed uniformly and smoothly throughout the material. However, the researchers theorized that these pairs might instead organize themselves into distinct, repeating spatial patterns.
Their theoretical model put forward a profoundly unusual prediction. Pair density waves could potentially survive at temperatures above the critical transition point, implying that Cooper pairs might spontaneously form even when a material had not yet entered its macroscopic superconducting phase.
"We were out on a limb when we first suggested it," Fradkin recalled. "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."
The experimental verification was complicated by the nature of the phenomenon itself. "PDWs are tricky to analyze in real materials, because they behave like conventional superconductors in some experiments, and like CDWs in others," noted Julian May-Mann, a former Illinois Grainger Engineering graduate student who contributed to 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 widely regarded by the scientific community as an ordinary, unexceptional metal. That perception changed dramatically when researchers discovered that it undergoes a transition into a superconducting phase when cooled below 2 kelvins.
Subsequent investigations led physicists to suspect that uranium ditelluride might be a rare example of a triplet-pair superconductor. Unlike the standard electron pairs described by classical BCS theory—which possess zero net spin—triplet electron pairs possess intrinsic magnetic moments.
Historically, the only thoroughly confirmed example of a triplet-pair ‘super-phase’ is superfluid helium-3. That complex system was extensively studied by the late Illinois physicist Anthony Leggett, whose foundational contributions earned him a Nobel Prize.
"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 intense focus of Madhavan’s experimental research group. Using advanced scanning tunneling microscopy, the team successfully identified charge density waves within the material. Yet, something about these observed waves defied expectations: they were acutely sensitive to magnetic fields and could be entirely destroyed by 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 needed access to significantly cleaner samples of uranium ditelluride. PDWs are notoriously delicate quantum states that require highly regular, defect-free crystal lattices to properly manifest.
External collaborators provided higher-quality samples generated through a newly refined molten flux growth method. The researchers then analyzed these pristine crystals using a sophisticated vector magnetic field scanning tunneling microscope, an instrument enabling scientists to examine how a material’s surface responds to magnetic fields applied from multiple, independent spatial directions.
"我们 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."
Zhen Zhu, an Illinois Grainger Engineering physics postdoctoral research associate who executed the physical experiments, emphasized the technical leap provided by the new apparatus. "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 with temperature and magnetic field strength precisely in the manner predicted for pair density waves. Crucially, magnetic effects were capable of destroying these modes, aligning neatly with the theoretical framework.
The most dramatic finding emerged when the researchers incrementally raised the temperature of the system. Certain observed modes continued to exist even after the material surpassed its critical temperature, pushing past the point where the main superconducting phase had entirely 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 observed. "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 research team remains mindful of certain methodological boundaries. Because scanning tunneling microscopy imaging is strictly limited to measuring effects at a material’s surface, the experiment does not directly reveal the microscopic dynamics occurring deep within the interior of uranium ditelluride. Nevertheless, the investigators maintain that these findings constitute a powerful indicator and will likely open unprecedented avenues for exploring 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 concluded.
Reflecting on the collaborative effort, Zhu added, "As an experimentalist, one of the most satisfying things is when several independent measurements begin to tell the same story. 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.
