Cross correlation mediated by Majorana island with finite charging energy

Abstract

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.

Master equation approach for transport through Majorana zero modes

“…Aside from conductance (tunneling spectroscopy) measurements, extensive considerations for inferring Majorana signatures from current power spectrum have been proposed [12,[35][36][37][38][39][40][41][42][43][44]. We noticed that most of these proposals considered the hybrid setup of coupling the MZMs to transport leads, not directly, but via quantum dots (QDs) [37][38][39][40][41][42][43][44], in order to avoid suppressing the Andreev reflection (AR) process in the absence of charging energy on the (grounded) Majorana island. For this type of setup, applying the master equation approach is most convenient, since one can follow the usual simple treatment of transport Figure 1.…”