Uranium Ditelluride Shows Cooper Pairs Persist Beyond Superconductivity

Physicists at the University of Illinois at Urbana-Champaign’s Granger Institute of Technology have found evidence of an unusual superconducting state in uranium ditelluride. Their experiments indicate that Cooper pairs—the electron pairs responsible for superconductivity—can form nonuniform patterns even after the material has left its primary superconducting phase.

These patterns are known as paired density waves (PDWs). Scientists first predicted PDWs about 20 years ago, and previous studies had observed them alongside superconductivity in other metals. The new research, published in Proceedings of the National Academy of Sciences, provides the first direct evidence that PDWs in uranium ditelluride can persist in the material’s “normal” phase after superconductivity disappears.

“Paired density waves are the grin of the superconducting Cheshire Cat,” said Eduard Fradkin, Illinois Grainger Professor of Engineering Physics and project co-leader. “They are the traces that remain after the phase itself disappears. In conventional superconductors, Cooper pairs form when a complete phase transition occurs, but in this system, the observation of Cooper pairs in the PDW above the transition point shows that they are formed in different states beforehand.”

“Thanks to our new method for growing higher-quality samples, we were able to observe spectral features that respond precisely to temperature and magnetic field, just as paired density waves should,” said Vidya Madhavan, a professor of physics at the Grainger School of Engineering at Illinois and another co-director of the project. “We even showed that the mode persists beyond the temperature at which superconductivity disappears, a theoretical prediction that provides evidence that has never been convincingly observed before.”

How unconventional superconductors work

Superconductivity occurs when a metal can conduct electricity with zero resistance after being cooled below a critical temperature. In this state, the material’s free electrons settle into a low-energy quantum state.

This creates a fundamental challenge. Electrons belong to a group of particles called fermions, and quantum mechanics prevents identical fermions from occupying the same state. Superconductivity circumvents this limitation through a process involving pairs of electrons.

In 1957, Illinois physicists John Bardeen, Leon Cooper and Robert Schrieffer explained this behavior with a theory known as BCS theory. According to the model, electrons become correlated through interactions with the underlying lattice of the metal. One electron then pairs with another, forming a Cooper pair.

Unlike individual electrons, Cooper pairs behave as bosons. Many bosons can occupy the same quantum state without the restrictions that apply to individual fermions. Once the pairs form, they condense together and produce superconductivity.

BCS theory successfully explained known superconducting behavior until scientists discovered an “unconventional” superconductor in 1986. These materials do not fit all the assumptions behind BCS theory, even though their electrons still form Cooper pairs and condense. Understanding how unconventional superconductors work remains an active area of physics research.

What are paired density waves?

Unconventional superconductors often host other electronic phases at temperatures below the superconducting critical temperature. One example is a charge density wave (CDW), in which electrons form a repeating, nonuniform pattern. The charge therefore changes periodically, with some regions containing more charge than others.

In 2007, Fradkin and his colleagues proposed another possible state known as a paired density wave. Although Cooper pairs are typically distributed evenly throughout a superconductor, the researchers suggested that the pairs could instead be arranged in a repeating pattern.

The theory made an unusual prediction: paired density waves could persist beyond the critical temperature. In other words, Cooper pairs could remain present even when the material was no longer superconducting.

“When we first proposed it, we were at a loss,” Fradkin said. “This is a very unique condition, and although there have been experimental hints, the existence of this state has not been directly confirmed.”

“PDWs are difficult to analyze in real materials because they behave like conventional superconductors in some experiments and like CDWs in others,” said Julian Mayman, a former Illinois Grainger Engineering graduate student who worked on the theoretical analysis of the study. “Confirming the existence of PDWs requires both high-quality experimental data and careful theoretical analysis.”

Why uranium ditelluride is unusual

Until 2019, uranium ditelluride was generally considered an ordinary metal. That changed when researchers discovered that it enters a superconducting phase below 2 kelvin.

Further investigation led physicists to suspect that uranium ditelluride could be a rare triplet-pairing superconductor. Unlike the electron pairs described by conventional BCS theory, triplet electron pairs have a magnetic moment.

The only confirmed example of a triplet-pairing “superphase” is superfluid helium-3. This system was extensively studied by the late Illinois physicist Anthony Leggett, who won a Nobel Prize for his work.

“It has been speculated that triplet-pairing superconductors with properties similar to superfluid helium-3 exist, and there are several superconductors that may be examples of this,” Fradkin said. “Although this issue is far from completely resolved, the consensus is that uranium ditelluride is a triplet superconductor.”

Uranium ditelluride eventually attracted the attention of Madhavan’s experimental research group. The researchers used scanning tunneling microscopy to identify a charge density wave in the material. However, the wave did not behave as expected: it could be destroyed by magnetic fields.

“A charge density wave is just a collection of electronic states modulated in space, so there is no reason for it to react to a magnetic field, much less be destroyed by a magnetic field,” Madhavan said. “We passed the data to Professor Fradkin and his students and predicted that this could happen if there were also pair density waves in the system. There aren’t many possible explanations for something like this, but pair density waves are the best explanation I can think of.”

Higher-quality crystals reveal hidden behavior

To investigate the possibility of paired density waves, Madhavan’s team first needed a cleaner sample of uranium ditelluride. PDWs are delicate and require highly ordered crystals to form.

Collaborators provided high-quality samples produced with a new fused-flux growth method. The researchers then examined the samples using vector magnetic-field scanning tunneling microscopy (STM). This technique allows scientists to study how a material’s surface responds to magnetic fields applied from different directions.

“We couldn’t see the pair density waves in our previous data because material impurities were obscuring the data,” Madhavan said. “It was like trying to find light in a cloud of fog. But thanks to the new vector magnetic-field instrument, we were able to obtain a better sample. The latter was especially important because uranium ditelluride is anisotropic, so we needed the ability to examine the crystal from multiple directions.”

“The main advantage of our experiment was the newly developed vector magnet device, which provides an unusually wide magnetic-field range along multiple directions,” said Zhen Zhu, a Grainger Engineering Physics postdoctoral fellow at Illinois who conducted the experiment. “This ability is particularly suited to uranium ditelluride, where the superconducting upper critical magnetic field is strongly anisotropic. By systematically varying both the magnitude and direction of the magnetic field with temperature, we can track how these modes evolve and build confidence that the behavior we observe is unique.”

Cooper pairs remain after superconductivity disappears

Measurements of the charge density wave revealed modes that changed with temperature and magnetic field in the way expected for paired density waves. As predicted by the PDW explanation, magnetic fields could destroy the modes.

The most striking results appeared when the researchers increased the temperature. Some modes continued to exist after the material exceeded its critical temperature and the primary superconducting phase disappeared.

“There are fundamental principles in condensed matter physics that constrain how different phases appear and disappear when you change temperature or apply a magnetic field,” Mayman said. “An explanation of the experimental data that relies solely on the CDW is inconsistent with these principles, whereas an explanation based on the PDW provides a satisfactory and consistent explanation.”

The researchers note an important limitation: STM imaging measures effects only at the material’s surface. As a result, the experiment cannot directly reveal what is happening throughout the interior of uranium ditelluride. Even so, the findings provide strong clues and could open new directions in research on unconventional superconductivity.

“Although it’s possible that the inside of the material behaves differently than the surface, these experimental results still give us very strong hints about what’s going on inside,” Fradkin said.

“One of the most satisfying things as an experimenter is when multiple independent measurements start telling the same story,” Zhu said. “Here, the temperature and magnetic-field dependence, as well as improved sample quality, all combine to reveal a surprisingly consistent picture of the paired density wave state.”

Yudi Huang, Kaiming Liu, Zheyu Wu, Shanta Saha, Johnpierre Paglione, Alexander Eaton, Andrej Cabala and Michal Vališka also contributed to the work.

Support was provided by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Division of Materials Science and Engineering.