Tunable Majorana corner modes in noncentrosymmetric superconductors: Tunneling spectroscopy and edge imperfections

Majorana corner modes appearing in two-dimensional second-order topological superconductors have great potential applications for fault-tolerant topological quantum computations. We demonstrate that in the presence of an in-plane magentic field two-dimensional ($s+p$)-wave superconductors host Majorana corner modes, whose location can be manipulated by the direction of the magnetic field. In addition, we discuss the effects of edge imperfections on the Majorana corner modes. We describe how different edge shapes and edge disorder affect the number and controllability of the Majorana corner modes, which is of relevance for the implementation of topological quantum computations. We also discuss tunneling spectroscopy in the presence of the Majorana corner modes, where a lead-wire is attached to the corner of the noncentrosymmetric superconductor. The zero-bias differential conductance shows a distinct periodicity with respect to the direction of the magnetic field, which demonstrates the excellent controllability of the Majorana corner modes in this setup. Our results lay down the theoretical groundwork for observing and tuning Majoran corner modes in experiments on ($s+p$)-wave superconductors.

出现在二维二阶拓扑超导体中的马约拉纳角模在容错拓扑量子计算方面具有巨大的潜在应用。我们证明，在存在面内磁场的情况下，二维（s + p）波超导体具有马约拉纳角模，其位置可由磁场方向操控。此外，我们讨论了边缘缺陷对马约拉纳角模的影响。我们描述了不同的边缘形状和边缘无序如何影响马约拉纳角模的数量和可控性，这与拓扑量子计算的实现相关。我们还讨论了存在马约拉纳角模时的隧道谱，此时将一根引线连接到非中心对称超导体的角上。零偏置微分电导相对于磁场方向呈现出明显的周期性，这表明在这种设置下马约拉纳角模具有出色的可控性。我们的结果为在（s + p）波超导体实验中观测和调控马约拉纳角模奠定了理论基础。