Influence of an embedded quantum dot on the Josephson effect in the topological superconducting junction with Majorana doublets

摘要

One Majorana doublet can be realized at each end of thetime-reversal-invariant Majorana nanowires. We investigate the Josephson effectin the Majorana-doublet-presented junction modified by different inter-doubletcoupling manners. It is found that when the Majorana doublets couple indirectlyvia a non-magnetic quantum dot, only the normal Josephson effects occur, andthe fermion parity in the system just affects the current direction andamplitude. However, in the odd-parity case, applying finite magnetic field onthe quantum dot can induce the appearance of the fractional Josephson effect.Next, when the direct and indirect couplings between the Majorana doubletscoexist, no fractional Josephson effect takes place, regardless of finitemagnetic field on the quantum dot. Instead, the $\pi$-period current has anopportunity to appear in some special cases. All the results are clarified byanalyzing the influence of the fermion occupation in the quantum dot on theparity conservation in the whole system. We ascertain that this work will behelpful for describing the dot-assisted Josephson effect between the Majoranadoublets.