Superconductivity remains one of the most fascinating quantum phenomena in condensed-matter physics. At low temperatures, electrons overcome their mutual Coulomb repulsion to form pairs known as “Cooper pairs,” enabling them to flow with zero electrical resistance. According to conventional Bardeen–Cooper–Schrieffer (BCS) theory, these pairs consist of electrons with opposite spins (spin-singlet state). However, an exotic state was later proposed where electrons with the same spin direction pair up—a phenomenon called spin-triplet superconductivity. Discovered in 1983, the heavy-fermion compound UBe₁₃ has long been considered a prime candidate for this triplet state. Yet, because of the extreme difficulty of growing high-quality single crystals and its anomalous normal- and superconducting-state behaviors, the exact nature of its superconductivity remained an unsolved mystery for over 40 years.

Definitively identifying a spin-triplet state requires measuring the magnetic susceptibility of the paired spins. However, standard macroscopic magnetization measurements fail because the immense Meissner effect—the diamagnetism caused by superconducting shielding currents—completely masks the subtle spin susceptibility. To overcome this experimental hurdle, nuclear magnetic resonance (NMR) was utilized. As a microscopic technique that uses the atomic nucleus as a local quantum probe, NMR suppresses the disruptive Meissner effect on a microscopic scale, enabling the intrinsic spin state of the Cooper pairs to be observed directly. Furthermore, measurements of the NMR relaxation rate enable the exact shape of the superconducting energy gap to be mapped out.

Through this sophisticated microscopic approach on high-quality UBe₁₃ single crystals (Tc = 0.85 K), the spin susceptibility and the superconducting energy gap were investigated in detail. The reduction patterns of the spin susceptibility definitively proved the realization of a spin-triplet superconducting state. Furthermore, NMR relaxation rate measurements revealed that UBe₁₃ possesses a highly unique multiband, nodeless (fully gapped) state. This means conducting electrons travel through multiple pathways (bands), and every single pathway features a complete energy barrier with no “loopholes” (nodes).

The combination of a spin-triplet state and a nodeless multiband gap defines an extremely rare phase called “topological spin-triplet superconductivity.” This state is theoretically predicted to host Majorana particles on the surface of the material. Because these particles are topologically protected against environmental noise and defects, they are highly sought after as ideal building blocks for fault-tolerant, next-generation quantum computers. This definitive proof in UBe₁₃ is expected to ignite a new wave of breakthroughs in quantum materials research.

(Written by Hideki Tou on behalf of the authors.)

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