Transport characterization of topological superconductivity in a planar Josephson junction

Inspired by two recent experiments in Nature [Fornieri et al., Nature (London) 569, 89 (2019); Ren et al., ibid. 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.