Current noise cross correlation mediated by Majorana bound states

TL;DR

This paper investigates how Majorana bound states influence noise cross correlations in a quantum dot-Majorana system, revealing voltage-dependent sign changes and particle-hole symmetry effects, using exact Green's function solutions and master equations.

Contribution

It provides an exact Green's function analysis of noise correlations in a Majorana hybrid system, highlighting conditions for positive and negative correlations and comparing with master equation results.

Findings

Noise cross correlation is negative at low voltages for symmetric levels.

Cross correlation becomes positive as lead voltage increases.

Particle-hole symmetry ensures always positive correlation in anti-symmetric case.

Abstract

We study the transport properties of a quantum dot-Majorana hybrid system, in which each of paired Majorana bound states is connected to one quantum dot. With the help of non-equilibrium Green's function method, we obtain an exact solution of the Green's functions and calculate the currents through the quantum dots and nonlocal noise cross correlation between the currents. As a function of dot energy levels $\epsilon_{1}$ and $\epsilon_{2}$, we find that for the symmetric level configuration $\epsilon_{1}=\epsilon_{2}$, the noise cross correlation is negative in the low lead voltage regime, while it becomes positive with the increase of the lead voltages. Due to the particle-hole symmetry, the cross correlation is always positive in the anti-symmetric case $\epsilon_{1}=-\epsilon_{2}$. In contrast, the cross correlation of non-Majorana setups is always positive. For comparison, we also perform the diagonalized master equation calculation to check its applicability. It is found that the diagonalized master equations work well in most regimes of system parameters. Nevertheless, it shows an obvious deviation from the exact solution by the non-equilibrium Green's function method when all eigenenergies of the dot-Majorana hybrid system and simultaneously the energy intervals are comparable to the dot-lead coupling strength.