Current noise cross correlation mediated by Majorana bound states

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 ǫ1 and ǫ2, we find that for the symmetric level configuration ǫ1 = ǫ2, 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 ǫ1 = −ǫ2. In contrast, the cross correlation of nonMajorana 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.PACS numbers: 03.75. Lm, 74.78.Na, 73.21.La I. INTRODUCTIONMajorana fermions, defined as fermions equivalent to own antiparticles, have been being hunted by high energy physicists for a long time.1-3 Recent years, the search of Majorana fermions has been shifted to solid-state systems, such as in the fractional quantum Hall system and p-wave superconductors.2-8 In particular, the Majorana bound states (MBSs) are predicted to appear at two ends of a semiconductor nanowire, in the proximity of an s-wave superconductor and under a proper magnetic field.9-17 The signatures for possible formation of a spatially separated pair of MBSs were reported in several experiments.18-22 Two well-separated MBSs can define a nonlocal fermion level and its occupation encodes a qubit. [5][6][7] This nonlocal topological qubit is immune to local perturbation and thus, has potential application in quantum information. However, for the same reason, it is of great challenge to coherently transfer and to read out the quantum information of the topological states. 7,17,23 It has been suggested that the MBSquantum dot hybrid system might be one of the solutions to the problem. 7,23,24 Up to now, various MBS-dot hybrid devices [23][24][25][26][27][28][29][30][31][32][33][34][35] have been proposed to detect existence of MBS,26,28,29 to modulate nonlocal correlation, 30-34 to estimate lifetime, 27 and to remove the effect of disorder. 35Therefore, it is important to investigate the transport properties of the MBS-dot hybrid systems. One of the fascinating properties of MBSs is that MBSs could induce nonlocal current cross correlation when they are coupled to mesoscopic circuits. [36][37][38][39][40][41] It has been shown that a positive cross correlation could be induced when MBSs coupl...

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