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(a) Schematic setup of an experiment in which two STM leads or normal leads are connected to a Top-JJ that supports the MFs. (b) Energy spectrum of the Top-JJ with chemical potential μ = −2t, which lies in the topological region. The two MFs, which are localized at the junction, interfere with each other and display a 4π oscillation. (c) DOS for electron part of the coupled MFs in the Top-JJ. Both even parity state and odd parity state show a parity-correlated 4π oscillation. (d) Energy spectrum of the Top-JJ with chemical potential μ = −2t + 5.7Δ, which lies in the trivial region, and the disorder strength w = 0.13t. In this case, there does not exist any MF that is localized at the junction. However, the trivial Andreev bound states occasionally touch with each other in the presence of disorder. In such situation, the trivial Andreev bound states behave like the Andreev bound states formed by the two MFs in panel (b). (e) DOS of the trivial Andreev bound states for the electron part. It is totally different from the DOS of the nontrivial Andreev bound states in panel (c). The period of the trivial state is 2π.
Source publication
We study theoretically the local density of states (DOS) in a topological Josephson junction. We show that the well-known 4π Josephson effect originates from the interference effect between two Majorana fermions (MFs) that are localized at the Josephson junction. In addition, the DOS for electrons (holes) shows the 4π interference information along...
Citations
... Therefore, considerable theoretical schemes have been proposed to reveal the clearly distinguishable fingerprints of MBSs during the past years [37][38][39][40][41]. One aspect is to concentrate on promising topological superconducting systems or prototypical models that support MBSs [42,43]. For the other aspect, special MBS-assisted transport behaviors have been explored by coupling them to some typical circuits [41]. ...
We theoretically study the quantum transport through a Fano-Rashba interferometer with an embedded Majorana doublet which generates at one end of the DIII-class topological superconductor. It shows that the Rasbha spin-orbit interaction in the reference arm drives the apparent and terminal-dependence spin polarization of the electron tunneling and crossed Andreev reflection, accompanied by their opposite directions. However, spin degeneracy holds in the local Andreev reflection. Next once the Majorana doublet is replaced by the Andreev bound state, the spin-polarization properties of the Andreev reflections are interchanged. Therefore, the Fano-Rashba interferometer can be a promising candidate for differentiating the Majorana doublet from other bound states.
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.
