Probing zero-modes of defect in Kitaev quantum wire

The Kitaev quantum wire (KQW) model with open boundary possesses two Majorana edge modes. When the local chemical potential on a defect site is much higher than that on other sites and than the hopping energy, the electron hopping is blocked at this site. We show that the existence of such a defect on a closed KQW also gives rise to two low-energy modes, which can simulate the edge modes. The energies of the defect modes vanish to zero as the local chemical potential of the defect increase to infinity. We develop a quantum Langevin equation to study the transport of KQW for both open and closed cases. We find that when the lead is contacted with the site beside the defect, we can observe two splitted peaks around the zero-bias voltage in the differential conductance spectrum. While if the lead is contacted with the bulk of the quantum wire far from the the defect or the open edges, we cannot observe any zero-bias peak.