Research On The Tunneling Transport And Spin Properties Through A System Of Quantum Dot With Majorana Fermions

We study the quantum transport properties through a system of quantum dots-Majorana fermion(MF), the differential conductance, spectral function and spin current can be achieved by using the retarded Green’s functions method. We discuss the calculation results in detail.Firstly, we studey the tunneling transport properties through a system of parallel quantum dots which are coupled to Majorana bound states. We consider the setup in which the up and down quantum dots are coupled to the ends of a semiconductor nanowire with strong Rashba spin-orbit interaction and proximity-induced s-wave superconductivity. The two quantum dots are connected to left and right normal leads, formed a configuration in parallel. Under the right conditions, Majorana fermion emerged in the end of the nanowire. For the convenience of expression, the up quantum dot is noted as dot1 and the down quantum dot refered as dot2. Similar to single quantum dot-Majorana fermion system, the conductance of each channel is 1/ 2(unit is2e/ h) at zero Fermion energy and is robust against the coupling between the Majorana fermion and quantum dots and the connecting of two quantum dots. The spectral function through the dot1 is considerably affected when the coupling between MF and dot2 is small. In contrast, when the coupling between MF and dot2 is large, the spectral function through dot2 is strongly influenced. Adjusting the coupling parameter of quantum dot and electrodes, the system can be changed from paralle to serial. For the configuration in series, the spectral function shows three peaks, and the three-peak structure evolves into a spectral function with two peaks in paralle. On the other hand, the conductance exhibits a quite different plateau when the Fermi energy is not zero. The conductance yields an asymmetrical line shape due to the interference of transportation of two channels when the coupling between two Majorana fermions is not zero.Secondly, we investigate the spin transport properties through a quantum dot coupling with Majorana fermion by applying a symmetric dipolar spin battery. It should be noted that due to the helical property of the MF states, only one of the quantum dot spin orientations(say spin-down) hybridizes with the MFs. The spin current and charge current increase as the coupling strength between the quantum dot and MF, but the resonant peaks become less sensitive to coupling strength. In the extreme case where the dot-MF coupling strength is large enough, the spin-down current saturates to a constant immune to the quantum dot energy, and the spin current and charge current obtain a limited value. We also investigate the influence of the Zeeman energy in the quantum dot, as the Zeeman energy increase, one of the resonance peaks is strongly suppressed. On the other hand, the coupling between two MFs can suppress the influence of the Majorana fermion.