Physicists at the University of Illinois Urbana-Champaign’s Grainger College of Engineering have broken new ground in the study of quantum materials, uncovering compelling evidence of an unusual form of superconducting behavior hidden within the heavy-fermion compound uranium ditelluride. Their rigorous experiments reveal that Cooper pairs—the fundamental bound pairs of electrons that make superconductivity possible—can arrange themselves into uneven, periodic patterns even when the material is no longer maintaining its primary macroscopic superconducting state.
These spatial arrangements are known as pair density waves, or PDWs. First theorized by physicists roughly two decades ago, PDWs have previously been observed coexisting alongside superconductivity in various other metals and high-temperature superconductors. However, the new research, which has been published in the Proceedings of the National Academy of Sciences, pushes past previous boundaries. It delivers the first direct experimental evidence that pair density waves in uranium ditelluride can survive within the material’s ordinary, non-superconducting phase long after full superconductivity has completely vanished.
"Pair density waves are the Cheshire Cat’s grin of superconductivity," said Eduardo Fradkin, a physics professor at the Illinois Grainger College of Engineering and a co-lead of the 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 measurement tools. "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
To understand the significance of this discovery, it helps to examine the mechanics of superconductivity itself. Superconductivity is a remarkable quantum phenomenon wherein a material—typically a metal—can carry electrical current with absolute zero resistance after being cooled below a specific critical temperature. In this zero-resistance state, the material’s free conduction electrons settle into a unified, low-energy quantum mechanical state.
This creates a fundamental physical challenge for nature. Electrons belong to a class of subatomic particles called fermions, and the foundational rules of quantum mechanics explicitly prohibit identical fermions from gathering in the exact same quantum state. Superconductivity manages to bypass this rigid restriction through a more complex, cooperative process involving pairs of electrons.
In 1957, legendary Illinois physicists John Bardeen, Leon Cooper, and Robert Schrieffer formulated a microscopic explanation for this behavior, which became universally known as BCS theory. According to their landmark model, electrons first become correlated through subtle electrostatic interactions with the metal’s underlying atomic lattice. Once correlated, one electron pairs with another to create what is known as a Cooper pair.
Unlike individual, solitary electrons, Cooper pairs behave physically as bosons. This distinction is crucial because quantum mechanics dictates that many bosons can occupy the very same quantum state simultaneously, entirely free from the mutual repulsion that governs individual fermions. Once paired up into bosons, these electrons can condense collectively into a macroscopic superconducting state that flows without friction.
BCS theory successfully explained virtually all known superconducting behavior for decades, right up until scientists discovered a new class of "unconventional" superconductors in 1986. These exotic materials stubbornly refuse to fit the neat assumptions and parameters underlying BCS theory, even though their electrons still somehow form Cooper pairs and manage to condense. Consequently, understanding the exact mechanisms behind how unconventional superconductors operate remains one of the most intensely active and challenging areas of modern condensed matter 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 prominent example is the charge density wave, or CDW, in which a subset of electrons spontaneously organizes into a repeating, nonuniform spatial pattern. The physical result is a periodic variation in electronic charge density across the material, leaving some microscopic regions containing higher concentrations of electric charge while others contain significantly less.
In 2007, Eduardo Fradkin and his academic colleagues proposed the existence of yet another potential electronic phase: the pair density wave. In a standard, textbook superconductor, Cooper pairs are distributed uniformly and smoothly throughout the material. Fradkin’s theoretical team suggested, however, that under the right conditions, these paired electrons might also arrange themselves into repeating, spatially modulated patterns.
Their theoretical work put forward a particularly bold and unusual prediction. They suggested that pair density waves could potentially survive and remain stable at temperatures sitting strictly above the critical temperature. If true, this would mean that Cooper pairs could successfully 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 difficulty lay in detection and analysis. "PDWs are tricky to analyze in real materials, because they behave like conventional superconductors in some experiments, and like charge density waves in other," explained Julian May-Mann, a former Illinois Grainger Engineering graduate student who performed crucial theoretical analysis for the study. "Confirming the existence of a PDW requires both high-quality experimental data as well as careful theoretical analysis."
Why Uranium Ditelluride Stands Out
Up until 2019, uranium ditelluride was widely viewed by the scientific community as a relatively ordinary metal. That perception shifted dramatically when researchers discovered that the compound enters a superconducting phase when cooled below a mere 2 kelvins.
Subsequent investigations quickly led physicists to suspect that uranium ditelluride might be a remarkably rare example of a triplet-pair superconductor. Unlike the standard electron pairs described by conventional BCS theory—which possess zero net spin—triplet electron pairs possess nonzero intrinsic magnetic moments.
Historically, the only definitively confirmed example of a triplet-pair quantum "super-phase" has been superfluid helium-3. That complex fluid system was extensively studied by the late Illinois physicist Anthony Leggett, whose foundational work ultimately 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 noted. "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 sharp focus of Madhavan’s experimental research group. Using advanced scanning tunneling microscopy, the team identified clear charge density waves within the material. Yet, something about the behavior of these waves defied standard expectations. When external magnetic fields were applied, the charge density waves were unexpectedly destroyed.
"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 rigorously investigate the hypothesis of pair density waves, Madhavan’s team first needed significantly cleaner, higher-purity samples of uranium ditelluride. Because PDWs are extraordinarily delicate electronic states, they require highly regular, defect-free crystal lattices in order to properly form and be observed.
Collaborators supplied these higher-quality samples, which were produced using a newly refined molten flux growth method. The researchers then examined the pristine samples using a state-of-the-art vector magnetic field scanning tunneling microscope. This specialized instrumentation allows scientists to observe with high precision how a material’s surface electronic structure responds to magnetic fields applied simultaneously from several different spatial 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."
The technical demands of the material made the specialized gear indispensable. "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 demanding laboratory 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
Detailed measurements of the charge density waves revealed distinct electronic modes that shifted in response to both temperature and magnetic fields in the exact manner theoretically predicted for pair density waves. Crucially, applying magnetic effects successfully destroyed them, directly matching the theoretical predictions.
The most striking and definitive result emerged when the researchers incrementally raised the temperature of the sample. Certain observed modes continued to exist stubbornly even after the material passed its critical temperature threshold and the primary, macroscopic superconducting phase had entirely disappeared from the system.
"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 to their work. Scanning tunneling microscopy imaging can only directly measure electronic effects occurring precisely at a material’s exposed surface. Consequently, the experiment does not directly reveal the microscopic phenomena unfolding deep within the bulk interior of the uranium ditelluride crystals. Even so, the research team remains confident that the surface findings offer a powerful window into the material’s inner physics and could open entirely new methodological 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 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.
