9/9/2026 Michael O'Boyle
Physicists with the University of Illinois Urbana-Champaign’s Grainger College of Engineering have identified a new form of superconducting behavior. Experiments on the metal uranium ditelluride reveal that Cooper pairs, the composite electron units responsible for superconductivity, can organize into nonuniform patterns that exist even when the main superconducting phase is absent.
Written by Michael O'Boyle
Physicists with the University of Illinois Urbana-Champaign’s Grainger College of Engineering have identified a new form of superconducting behavior. Experiments on the metal uranium ditelluride reveal that Cooper pairs, the composite electron units responsible for superconductivity, can organize into nonuniform patterns that exist even when the main superconducting phase is absent.
These patterns, known as pair density waves (PDWs), were first predicted 20 years ago and have been found to coincide with superconductivity in other metals. But new research published in the Proceedings of the National Academy of Sciences not only shows that PDWs exist in uranium ditelluride, but it provides the first direct evidence that they can persist in the “ordinary” phase once superconductivity vanishes.
“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.”
Unconventional superconductors
The phenomenon of superconductivity, in which metals conduct electricity with zero resistance, arises because the metal’s free electrons condense into a low-energy quantum state when cooled below a critical temperature. However, electrons belong to a class of particles called fermions, meaning the laws of quantum physics prohibit them from coalescing into the same state. The mechanism by which they are allowed to condense in superconductivity is complex and subtle.
This complexity was first explained in 1957 by Illinois physicists John Bardeen, Leon Cooper and Robert Schrieffer in a model now known as the BCS theory. They proposed that electrons condense by first correlating through the metal’s underlying lattice. Each electron binds to another electron, forming units called Cooper pairs. Unlike single electrons, Cooper pairs belong to a class of particles called bosons, so they can coexist in the same state with no quantum repulsion. The pairs are then free to condense into the superconducting state.
BCS theory successfully accounted for all observed superconducting behavior until “unconventional” superconductors were identified in 1986. Their structures are incompatible with the assumptions of BCS theory, but electrons still form Cooper pairs and condense. Understanding the properties of unconventional superconductors remains an active area of research.
Pair density waves
A feature that unconventional superconductors seem to have in common is the cooccurrence of other phases below the superconductivity critical temperature. One example is charge density waves (CDWs), in which a fraction of the electrons organizes into nonuniform patterns. Since the charge density modulates periodically in space, there are regions with more electric charge and regions with less electric charge.
In 2007, Fradkin and his colleagues proposed another example of a cooccurring phase: pair density waves. Ordinarily, superconducting Cooper pairs are uniformly distributed in the metal, but the Illinois theorists suggested that they can also organize into patterns. One of the most striking predictions of their theory is that PDWs can exist above the critical temperature, implying that Cooper pairs can form even when the metal is not in the 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.
Uranium ditelluride: the odd metal out
Until 2019, uranium ditelluride was thought to be an ordinary metal, so researchers took note when a superconducting phase below 2 kelvins was discovered. As it was studied, physicists started to believe that it was an elusive triplet-pair superconductor. Unlike pairs in BCS superconductors triplet electron pairs have magnetic moments. The only confirmed instance of a triplet-pair ‘super-phase’ is superfluid helium-3. This system was studied extensively by late Illinois physicist Anthony Leggett, who was awarded 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.”
The metal attracted the attention of Madhavan’s experimental research group, which identified CDWs using scanning tunneling microscopy experiments. However, the researchers noticed something peculiar: the waves could be destroyed using magnetic fields.
“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.”
Vanishing modes
To investigate, Madhavan’s group first needed to obtain higher quality samples of uranium ditelluride. PDWs are very delicate and can only form in highly regular crystals. The researchers turned to collaborators to provide high-quality samples grown using a new molten flux method. These samples were studied using a vector magnetic field scanning tunneling microscope (STM), an instrument that probes the responses of material surfaces to magnetic fields in arbitrary 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.”
The data on CDWs revealed modes that responded to temperature and magnetic field just as PDWs should, including their destruction with magnetic effects. But most telling, there were modes that continued to exist above the critical temperature when the main superconducting phase no longer existed.
“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.”
Although STM imaging can only characterize surface effects, the researchers are encouraged by their findings and optimistic that the result points to new directions of research.
“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.
The study, “Evidence of intertwined pair density and charge density wave orders in UTe2,” is available online. DOI: 10.1073/pnas.2602117123
Support was provided by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division.
Illinois Grainger Engineering affiliations
Eduardo Fradikin is a professor in the Department of Physics. He is the Director of The Anthony J. Leggett Institute for Condensed Matter Theory, and he is affiliated with the Materials Research Laboratory and the Illinois Quantum Information Science and Technology Center. He holds a Donald Biggar Willett Professor in Engineering appointment.
Vidya Madhavan is a professor in and the Department Head for the Department of Physics. She is affiliated with the Materials Research Laboratory and the Illinois Quantum Information Science and Technology Center. She holds a Donald Biggar Willett Professor in Engineering appointment.