Inspired by two recent experiments in Nature [Fornieri et al., Nature (London) 569, 89 (2019); Ren et al., Nature (London) 569, 93 (2019)], we numerically studied the transport properties of topological superconductivity in a planar Josephson junction. Our numerical calculations suggest that the origin of a zero-bias conductance peak is not unique. In addition to the single pair of Majorana zero modes, multiple pairs of Majorana zero modes can also exist at the ends of the junction. Although the bulk energy spectra in these two regions are distinguished, the signal measured through conductance cannot reveal the true information of the bulk energy spectrum. Thus the zero-bias conductance peaks measured in both two regions are quite similar and are hard to distinguish. In order to reveal the right information regarding the topological region, more methods in addition to the local conductance measurements are needed. Moreover, these multiple Majorana zero modes are not stable and fragile for topological quantum computation. To realize a topological Josephson junction with stable Majorana zero modes, the junction width should be smaller than half of the superconducting coherence length, and the superconducting bulk width should be larger than the coherence length.

中文翻译：

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平面约瑟夫森结中拓扑超导的输运表征

受到《自然》杂志上两项最新实验的启发[Fornieri等。，自然（伦敦） 569，89（2019）; 任等人。，大自然（伦敦） 569，93（2019）]，我们用数值方法研究了平面约瑟夫逊结中拓扑超导的传输特性。我们的数值计算表明，零偏置电导峰的起源不是唯一的。除了单对的马约拉纳零模式外，在结的末端还可以存在多对马约拉纳零模式。尽管这两个区域的整体能谱是有区别的，但通过电导测量的信号无法揭示整体能谱的真实信息。因此，在两个区域中测得的零偏置电导峰非常相似，难以区分。为了揭示有关拓扑区域的正确信息，除了局部电导测量之外，还需要更多的方法。此外，对于拓扑量子计算，这些多个Majorana零模式不稳定且脆弱。为了实现具有稳定的Majorana零模式的拓扑约瑟夫森结，结宽应小于超导相干长度的一半，而超导体宽应大于相干长度。