  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.
