These intricate spatial arrangements are known as pair density waves, or PDWs. First theorized by physicists approximately two decades ago, PDWs have previously been observed coexisting alongside conventional superconductivity in other metallic systems. However, this new research, recently published in the Proceedings of the National Academy of Sciences, pushes the boundaries of condensed matter physics much further. It provides the very first direct experimental evidence that pair density waves in uranium ditelluride can survive and persist 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 cutting-edge material synthesis and advanced 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 conduct electric current with absolute zero electrical resistance. In this highly ordered state, the material’s free electrons settle into a collective, low-energy quantum state.
This process presents a fundamental challenge under the laws of physics. Electrons belong to a class of subatomic particles known as fermions. Quantum mechanics strictly dictates that fermions cannot occupy or crowd into the exact same quantum state—a principle known as the Pauli exclusion principle. Superconductivity cleverly bypasses this restrictive rule through a more complex cooperative mechanism involving pairs of electrons.
In 1957, legendary Illinois physicists John Bardeen, Leon Cooper, and Robert Schrieffer formulated a revolutionary framework to explain this behavior, which became globally celebrated as BCS theory. According to their model, individual electrons first become correlated through delicate interactions with the metal’s underlying atomic lattice. Once linked, one electron binds with another to create what is known as a Cooper pair.
Unlike individual fermions, Cooper pairs behave collectively as bosons. This distinction is crucial because bosons are exempt from the Pauli exclusion principle, meaning a vast multitude of them can occupy the exact same quantum state without the intense mutual repulsion that normally separates individual electrons. Once paired, these bosons condense together into a unified macroscopic quantum state, giving rise to frictionless superconductivity.
BCS theory successfully accounted for nearly all known superconducting phenomena for decades, until scientists discovered a new class of "unconventional" superconductors in 1986. These exotic materials stubbornly refuse to fit the fundamental assumptions underlying BCS theory, even though their constituent electrons still manage to form Cooper pairs and condense. Decoding the precise mechanisms that govern how unconventional superconductors operate remains one of the most active and intensely pursued areas of modern physics research.
The Mystery of Pair Density Waves
Unconventional superconductors frequently host alternative electronic phases at temperatures below their superconducting critical transition temperature. One prominent example is charge density waves, or CDWs, in which electrons spontaneously form a repeating, nonuniform spatial pattern. The resulting state features a periodic variation in electrical charge, creating localized regions within the material that contain a higher density of electric charge alongside other regions containing less.
In 2007, Professor Fradkin and his research colleagues proposed the existence of another hypothetical phase known as a pair density wave. While Cooper pairs are normally distributed uniformly and homogeneously throughout a standard superconductor, the researchers hypothesized that these pairs might also spontaneously organize themselves into repeating spatial modulations.
Their theoretical work put forward a particularly provocative and unusual prediction: pair density waves could potentially survive and operate at temperatures above the critical transition point, implying that Cooper pairs might be capable of forming 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."
"PDWs are tricky to analyze in real materials, because they behave like conventional superconductors in some experiments, and like CDWs in others," added Julian May-Mann, a former Illinois Grainger Engineering graduate student who contributed significantly 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 a relatively ordinary metal. That perception shifted dramatically when researchers discovered that it undergoes a transition into a superconducting phase when cooled below 2 kelvins.
Further investigation quickly led physicists to suspect that uranium ditelluride might be a rare example of a triplet-pair superconductor. Unlike the spin-singlet electron pairs described by conventional BCS theory—where the paired electron spins point in opposite directions—triplet electron pairs possess parallel spins and non-zero magnetic moments.
Historically, the only definitively 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 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 keen attention of Madhavan’s experimental research group. Utilizing scanning tunneling microscopy, the team identified charge density waves within the material. However, something about the behavior of these charge waves defied standard expectations. Most notably, applied magnetic fields could entirely 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 noted. "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 possibility of pair density waves, Madhavan’s team first needed substantially cleaner and more uniform samples of uranium ditelluride. PDWs are exceptionally delicate quantum states that require highly regular crystalline structures to manifest clearly.
Collaborating researchers supplied higher-quality samples produced using an innovative molten flux growth method. The experimental team then examined these pristine crystals using a vector magnetic field scanning tunneling microscope, an advanced instrument that allows scientists to observe precisely how a material’s surface electronic structure responds to magnetic fields applied from multiple, independently controlled directions.
"We couldn’t see pair density waves in our earlier data because of material impurities that obscured our measurements," 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."
"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 detailed 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 precision measurements of the charge density waves revealed electronic modes that shifted in response to temperature and magnetic fields in the exact manner predicted for pair density waves. Crucially, magnetic effects were able to suppress and destroy them, aligning seamlessly with the theoretical framework.
The most striking and definitive result emerged when the researchers elevated the temperature of the samples. Several of these observed modes continued to exist even after the material passed its critical temperature threshold and the primary macroscopic superconducting phase had completely vanished.
"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 acknowledge an important experimental limitation: scanning tunneling microscopy imaging only measures electronic effects occurring at a material’s surface, meaning the experiment does not directly reveal the microscopic behavior happening deep within the interior of uranium ditelluride. Nevertheless, the research team is confident that the findings offer a powerful window into the material’s physics and could open entirely new research avenues 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 emphasized.
"As an experimentalist, one of the most satisfying things is when several independent measurements begin to tell the same story," Zhu concluded. "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.
