Transport Properties Of The Hybrid Majorana-superconductor System

Non-Abelian fermions have attracted much attention because of their potential applications in topological quantum computation.One common physical entity obeying non-Abelian statistics is the zero-energy Majorana fermion.For this reason,researchers have done a series of theoretical calculations and experiments to detect the nature of the Majorana fermion.In this work,in order to investigate the influence of Majorana fermions on transport properties,we use non-equilibrium Green's function method to study the transport properties of four pairs of Majorana fermions coupling with a quantum dot.For comparison,we also calculate the transport properties of a quantum dot without coupling.First,we studied the change curve of the superconducting current under the superconducting-normal mixed four-terminal electrode.The result show that Majorana fermions have a modulating effect on the current at the superconducting terminal.One interesting phenomenon is that the current with the N2 side of the bias curve appears on a peak,which is the result of the interference between Majorana fermions.Secondly,we studied the change of the normal side current under the superconducting-normal hybrid four-terminal electrode.We found that the variation of the N2-terminal current with the phase becomes 4?.Further exploration of this phenomenon leads to the existence of Majorana fermions in the system,and the coupling between the Majorana fermions can not be zero,and the N2-side current will have a 4? period.This may be a way to detect Majorana fermions.Finally,in order to better achieve Majorana fermions detection on the experiment,we try to decouple the N4 electrode into a three-terminal electrode,calculate the N2-side current change period,and find the period is 2?.So only in the four ends of the electrode can occur 4? cycle.