  Based on the many-particle-number-state treatment for transport through a
pair of Majorana zero modes (MZMs) which are coupled to the leads via two
quantum dots, we identify that the reason for zero cross correlation of
currents at uncoupling limit between the MZMs is from a degeneracy of the
teleportation and the Andreev process channels. We then propose a scheme to
eliminate the degeneracy by introducing finite charging energy on the Majorana
island which allows for coexistence of the two channels. We find nonzero cross
correlation established even in the Majorana uncoupling limit (and also in the
small charging energy limit), which demonstrates well the teleportation or
nonlocal nature of the MZMs. More specifically, the characteristic structure of
coherent peaks in the power spectrum of the cross correlation is analyzed to
identify the nonlocal and coherent coupling mechanism between the MZMs and the
quantum dots. We also display the behaviors of peak shift with variation of the
Majorana coupling energy, which can be realized by modulating parameters such
as the magnetic field.
