物理学进展

物理学进展 ›› 2025, Vol. 45 ›› Issue (5): 250-259.doi: 10.13725/j.cnki.pip.2025.05.003

• • 上一篇    

多轨道超导体中自旋轨道耦合导致的偶然零模

向 柯 1，王 达 1, 2 ∗，王强华 1, 2 †    

  1. 1. 南京大学物理学院，固体微结构物理国家重点实验室，南京 210093; 2. 南京大学人工微结构科学与技术协同创新中心，南京 210093
  • 出版日期:2025-10-20 发布日期:2025-10-24
  • 基金资助:
    国家重点研发计划(No. 2022YFA1403201) , 国家自然科学基金 (No. 12374147, 12274205 and 92365203). 

Accidental zero modes in a multiorbital superconductor with spin-orbital coupling 

XIANG Ke 1 , WANG Da 1, 2 ∗ , WANG Qianghua 1, 2 †    

  1. 1. National Laboratory of Solid State Microstructures & Department of Physics, Nanjing University, Nanjing 210093, China;  2. Collaborative Innovation Center of Advanced Microstructures, Nanjing 210093, China
  • Online:2025-10-20 Published:2025-10-24
  • Supported by:
    National Key R&D Program of China (Grant No. 2022YFA1403201) and National Natural Science Foundation of China (Grant No. 12374147, 12274205 and 92365203). 

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摘要：

在拓扑量子计算的背景下, 涡旋芯中的马约拉纳零模引起了广泛关注。然而，零能束缚态 可能偶然出现，并不一定是马约拉纳零模。在实验中必须仔细排除这类偶然零模，以识别真正的 马约拉纳零模。我们的研究表明，在自旋轨道耦合的多带超导体（如铁硒基超导体）中，如果配 对对称性是无节点 d 波（在无自旋轨道耦合的情况下定义），那么涡旋芯中确实会出现偶然零模。 反之，如果配对对称性相对于自旋轨道耦合分裂的费米口袋是 s++ 或 s±，那么在弱自旋轨道耦 合极限下，偶然零模不会出现。我们的结果不仅对马约拉纳零模的实验识别至关重要，也为确定 铁硒基超导体的配对对称性提供了一条途径。

关键词: 自旋轨道耦合, 安德烈夫近似, 偶然零模

Abstract:

The Majorana zero modes in vortex cores are of extensive interest in the context of topological quantum computing. However, a zero-energy bound state may arise accidentally but is not necessarily a Majorana zero mode. Such accidental zero modes should be carefully ruled out in experiment in order to identify the genuine Majorana zero modes. We show that in a spin-orbital coupled multi-band superconductor, such as the iron-selenide superconductor, accidental zero modes indeed arise in the vortex core if the pairing symmetry is the so-called nodeless d-wave (defined in the absence of spin-orbital coupling). Instead, if the pairing symmetry is s++ or s± with respect to the Fermi pockets split by the spin-orbital coupling, the accidental zero modes do not appear in the limit of weak spin-orbital coupling. Our results are not only important in the experimental identification of Majorana zero modes, but also provide an avenue to pinpoint the pairing symmetry of the iron-selenide superconductor.