Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA.
Department of Physics, Toho University, Funabashi, Japan.
Nature. 2021 Nov;599(7883):51-56. doi: 10.1038/s41586-021-03915-3. Epub 2021 Nov 3.
Charged particles subjected to magnetic fields form Landau levels (LLs). Originally studied in the context of electrons in metals, fermionic LLs continue to attract interest as hosts of exotic electronic phenomena. Bosonic LLs are also expected to realize novel quantum phenomena, but, apart from recent advances in synthetic systems, they remain relatively unexplored. Cooper pairs in superconductors-composite bosons formed by electrons-represent a potential condensed-matter platform for bosonic LLs. Under certain conditions, an applied magnetic field is expected to stabilize an unusual superconductor with finite-momentum Cooper pairs and exert control over bosonic LLs. Here we report thermodynamic signatures, observed by torque magnetometry, of bosonic LL transitions in the layered superconductor BaNbS. By applying an in-plane magnetic field, we observe an abrupt, partial suppression of diamagnetism below the upper critical magnetic field, which is suggestive of an emergent phase within the superconducting state. With increasing out-of-plane magnetic field, we observe a series of sharp modulations in the upper critical magnetic field that are indicative of distinct vortex states and with a structure that agrees with predictions for Cooper pair LL transitions in a finite-momentum superconductor. By applying Onsager's quantization rule, we extract the momentum. Furthermore, study of the fermionic LLs shows evidence for a non-zero Berry phase. This suggests opportunities to study bosonic LLs, topological superconductivity, and their interplay via transport, scattering, scanning probe and exfoliation techniques.
受磁场作用的带电粒子会形成朗道能级（LLs）。最初在金属中的电子背景下进行研究，费米子 LLs 继续作为奇异电子现象的宿主吸引着人们的兴趣。玻色子 LLs 也有望实现新的量子现象，但除了最近在合成系统方面的进展外，它们仍然相对未被探索。超导体内的库珀对——由电子组成的复合玻色子——代表了玻色子 LLs 的潜在凝聚态平台。在某些条件下，预期外加磁场将稳定具有有限动量库珀对的非常规超导体，并对玻色子 LLs 进行控制。在这里，我们通过转矩磁强计报告了在层状超导体 BaNbS 中观察到的玻色子 LL 跃迁的热力学特征。通过施加面内磁场，我们观察到在上临界磁场以下突然出现部分抗磁性的抑制，这表明超导态内出现了一个新相。随着外磁场的增加，我们观察到上临界磁场的一系列尖锐调制，这些调制表明存在不同的涡旋状态，其结构与有限动量超导体中库珀对 LL 跃迁的预测一致。通过应用 Onsager 的量子化规则，我们提取了动量。此外，对费米子 LLs 的研究表明存在非零的 Berry 相位。这表明有机会通过传输、散射、扫描探针和剥离技术研究玻色子 LLs、拓扑超导及其相互作用。
