Abstract

In the framework of the Bogoliubov-de Gennes theory, we investigate the Majorana zero-energy states in mesoscopic superconducting square systems with spin–orbit (SO) interaction. The mixed d-wave and extended s-wave condensates as well as the favored \(s+id\) state can be obtained by suitable choice of model parameters. We find that the energy gap is highly sensitive to the introduced SO interaction and the Majorana zero modes can emerge at four outer corners of a perfect square with only the Rashba SO interaction or with combined Rashba and Dresselhaus SO couplings. Furthermore, for a square sample with a centered hole, energy levels can cross the Fermi energy at appropriate Rashba SO-coupling strengths, accompanied with the occurrence of additional four Majorana corner states localized around the inner corners of the loop. The effect of Dresselhaus SO interaction on the number and location of Majorana corner states is also examined, and novel zero-energy modes mainly located at four opposite inner and outer corners along the (anti-)diagonal direction of the square loop can be realized.

Graphical abstract

中文翻译：

---

存在自旋轨道相互作用的混合配对介观超导方形系统中的马约拉纳角模式

摘要

在 Bogoliubov-de Gennes 理论的框架下，我们研究了具有自旋轨道 (SO) 相互作用的介观超导方形系统中的马约拉纳零能态。混合的d波和扩展的 s波凝聚以及受欢迎的\(s+id\)state can be obtained by suitable choice of model parameters. 我们发现能隙对引入的 SO 相互作用高度敏感，并且马约拉纳零模式可以出现在仅具有 Rashba SO 相互作用或组合 Rashba 和 Dresselhaus SO 耦合的完美正方形的四个外角。此外，对于具有中心孔的方形样品，能级可以在适当的 Rashba SO 耦合强度下穿过费米能量，并伴随着出现在环内角周围的额外四个马约拉纳角状态。还研究了 Dresselhaus SO 相互作用对马约拉纳角状态的数量和位置的影响，并且可以实现主要位于沿方形环的（反）对角方向的四个相对的内角和外角的新型零能量模式。

图形概要