Current noise cross correlation mediated by Majorana bound states

We study the transport properties of a quantum dot-Majorana hybrid system, in which each of the paired Majorana bound states is connected to one quantum dot. With the help of the nonequilibrium 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 antisymmetric 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 nonequilibrium 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.