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Two majorana Fermions (MFs) localized at the two ends of the topologicalsuperconducting wire can interfere with each other and form the well known$4\pi$ Josephson current. We reveal that the density of states (Dos) for theelectron part and the hole part also follow a parity correlated $4\pi$ periodoscillation, while the Dos displays a $2\pi$ period oscillation when twotrivial states interfere with each other. Thus, the period of Dos oscillationcan be used to distinguish the MFs from the trivial localized states.Interestingly, such phenomena can be directly observed in a shortsuperconducting wire controlled by the gate voltage. This largely simplifiesthe experimental setup. We suggest that the interference effects can bedetected through two STM leads or two norm leads.

Interference Effect of Majorana Fermions in a Spin-orbit Coupled Superconducting Wire