Cross-correlation mediated by Majorana island with finite charging energy

TL;DR

This paper investigates how finite charging energy on a Majorana island enables nonzero current cross correlations mediated by Majorana zero modes, revealing their nonlocal and coherent nature through spectral analysis.

Contribution

It introduces a scheme to lift degeneracy in Majorana systems using charging energy, demonstrating nonlocal correlations even when Majorana modes are uncoupled.

Findings

Finite charging energy induces nonzero cross correlation.

Spectral peaks reveal nonlocal coupling mechanisms.

Peak shifts correlate with Majorana coupling 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.