The first comprehensive characterization of unconventional superconductivity arising from multipolar moments

Superconductivity is a quantum phenomenon, observed in some materials, that entails the ability to conduct electricity with no resistance below a critical temperature. Over the past few years, physicists and material scientists have been trying to identify materials exhibiting this property (i.e., superconductors), while also gathering new insights about its underlying physical processes.

Superconductors can be broadly divided into two categories: conventional and unconventional superconductors. In conventional superconductors, electron pairs (i.e., Cooper pairs) form due to phonon-mediated interactions, resulting in a superconducting gap that follows an isotropic s-wave symmetry. On the other hand, in unconventional superconductors, this gap can present nodes (i.e., points at which the superconducting gap vanishes), producing a d-wave or multi-gap symmetry.

Researchers at the University of Tokyo recently carried out a study aimed at better understanding the unconventional superconductivity previously observed in a rare-earth intermetallic compound, called PrTi₂Al₂₀, which is known to arise from a multipolar-ordered state. Their findings, published in Nature Communications, suggest that there is a connection between quadrupolar interactions and superconductivity in this material.

“Under the microscope of quantum materials, the basic building block is the electron, which has microscopic charge spin, and orbital degrees of freedom,” Mingxuan Fu, co-author of the paper, told Phys.org. “When electrons are packed together in enormous numbers in a material, their various degrees of freedom can interact in intricate and fascinating ways, creating an incredibly diverse landscape of properties governed by quantum mechanics. Among those, the arguably most exemplified one is unconventional superconductivity.”

While many previous studies have tried to uncover the origins of unconventional superconductivity, its underlying driving force remains poorly understood. A conclusive answer to this long-standing research question could open new possibilities for the further advancement of quantum technologies.

“Traditionally, the field heavily focused on understanding the role of electron spins in generating and shaping unconventional superconductivity,” said Satoru Nakatsuji, the corresponding author of the paper. “However, as research progresses, it becomes clear that this puzzle is much richer and more complex than we initially thought. Other ingredients, such as orbital and charge, can also play a vital role, and their involvement could open new possibilities for novel superconductivity.”

Building on their previous research efforts, Fu, Nakatsuji and their colleagues set out to design a new superconductor, presenting a superconductivity emerging from something other than electron spin dynamics. Specifically, they hoped to determine whether superconductivity could also be produced by leveraging high-order multipolar moments, without electron spins.

“In this work, we focused on exploring a unique quantum phase where superconductivity emerges from a pure ferroquadrupolar order—high-order quadrupoles align uniformly in an ordered array across the material, similar to how spins align in a ferromagnetic state, but in this case, the ordering involves only quadrupoles without any spins,” said Akito Sakai, lead author of the paper.

“Our goals were to understand how the ferroquadrupolar order ties in with the emergence of superconductivity and how it influences the way electron pairs form and interact in the superconducting state.”

The new superconductor examined as part of this study, namely PrTi₂Al₂₀, was previously designed by the researchers. When this material is in its lowest energy state, which is the state in which quantum effects dominate, high-order quadrupolar and octopolar moments are active, while magnetic dipolar moments (i.e., spins) are absent.

“This feature provides an unmatched advantage in investigating superconductivity driven by multipolar moments,” explained Nakatsuji. “Working on this material brings immense intellectual pleasure, as it is very rare to encounter such a clean model platform for studying multipolar physics.”

Detecting and studying multipole-driven physical phenomena is typically very challenging. This is mainly because contrarily to spin-driven effects, which can be easily observed using widely available experimental probes, these phenomena are often far more difficult to pick up.

“There hasn’t been a single, decisive method to study multipolar phenomena,” said Nakatsuji. “That’s why in our study, we employed several experimental techniques, from heat capacity and DC magnetization to resistivity. We also explored how the ferroquadrupolar and superconducting phases evolved with chemical doping. Some of these experiments are incredibly challenging, as we need to reach the ultralow temperature regime (down to about -273 °C).”

Using a carefully selected set of techniques, the researchers were able to approach this problem from different angles, ultimately creating a coherent overall picture of what drives superconductivity in PrTi₂Al_20. Their paper was the first to provide a comprehensive characterization of unconventional superconductivity arising from multipolar moments.

“The superconducting behavior we observed is in no way similar to the conventional superconductivity explained by the textbook Bardeen- Cooper-Schrieffer (BCS) theory,” explained Sakai. “Such distinctions from BCS superconductivity stem from novel pairing symmetry—an unusual pattern in which electron pairs interact in the superconducting states.”

Overall, the researchers showed that the evolution of superconductivity driven by chemical doping is strikingly different from that emerging from spin fluctuations. This study could soon pave the way for further research focusing on this specific type of superconductivity, which could help to validate the team’s results and eventually contribute to the development of new quantum technologies.

“Through the chemical doping dependence, we found that the ferroquadrupolar order and the symmetry of the superconducting pairing are tightly linked, offering new insights into how superconductivity and multipolar order dance together and influence each other,” said Fu. “This work has greatly motivated us to delve deeper into the untapped realm of multipole-induced quantum phases and properties, pinpointing their key differences from spin-driven counterparts, such as new types of strange metals or quantum criticality.”

By further investigating multipole-induced quantum states, the researchers hope to eventually devise a new theoretical framework that better describes these phenomena and their underlying physics, potentially opening up a new pathway towards high-temperature superconductivity. Notably, multipoles have become the focus of a growing number of studies, and this research team’s efforts could play a key role in their future practical application.

“The concept of multipoles has gained solid ground in quantum materials research, and its spectrum of influence has been expanding rapidly in recent years, for instance, in understanding the functionalities of topological antiferromagnets,” added Nakatsuji.

“Experimentally probing quantum phenomena driven by atomic multipoles as a physical entity gives us a powerful and inspiring guide. This guide can lead us far in harnessing the unique quantum properties of multipoles, driving new scientific discoveries and innovative applications that push beyond the traditional spin-dominated paradigm.”

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