Abstract
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 each parity conserved energy spectrum. The DOS displays a 2π period oscillation when two trivial states interfere with each other. This means that the DOS information may be used to distinguish the MFs from trivial localized states. We suggest that the interference effect and the DOS can be detected by using two STM leads or two normal leads. A single side lead can only detect the Andreev reflection tunneling process in the junction, which cannot reveal information about the interference effect in general. However, using two side leads, we can reveal information about the interference effect of the MFs as well as the DOS by combining Andreev reflection with the electron transmission process.
Highlights
After Kitaev reported that Majorana fermions (MFs) can appear as quasi-particle states at the ends of a one-dimensional (1D) p-wave superconductor [1], the generation of MFs became a popular goal in condensed matter physics [2]
We show that a single side lead can only detect the Andreev reflection tunneling process in the junction, which cannot reveal information about the interference effect in general
We have shown that the main features of the density of states (DOS) for the nontrivial Andreev bound states are parity-correlated with a 4π period, which is very different from the trivial case
Summary
After Kitaev reported that Majorana fermions (MFs) can appear as quasi-particle states at the ends of a one-dimensional (1D) p-wave superconductor [1], the generation of MFs became a popular goal in condensed matter physics [2]. We show that the two Andreev bound states formed by the MFs exhibit a 4π period due to the interference effect between the two MFs. the DOS of both the electron and the hole part can reveal the 4π period.
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