Research On The Quantum Transport Through A System Of Quantum Dot With Majorana Fermions

In recent years Majorana fermions(MFs) have attracted much attention because they are their own antiparticles and obey the non-Abelian statistics. We know that an important way to detect the Majorana bound states(MBSs) is to study the transport through a quantum dot(QD) structure coupled with the MBSs. In this paper, we study the electron transport through structures including QD and MBSs using the nonequilibrium Green’s function technique.In the first chapter, we introduce the basic concepts and basic theory of QD and mesoscopic transport. In addition, we summarize the basic properties of Majorana fermion and the three types of transport processes simply. Finally we introduce the research status of Majorana fermion. In the second chapter, we make a brief introduction about the nonequilibrium green’s function method including its definition, the expression form in the Nambu representation, fluctuation-dissipation theorem, Langreth theorem, equations of motion, Dyson equations, Generalized Landauer-Buttiker formula.In Chapter 3, we study the electron transport through an Aharonov-Bohm ring composed of three QDs and two MBSs using the nonequilibrium Green’s function technique. This QDMBS ring includes two channels with the two coupled MBSs being Channel 1 and a QD being Channel 2, and three types of transport processes including the electron transmission(ET), the Andreev reflection(AR), the crossed Andreev reflection(CAR). By comparing the ET, AR, and CAR processes through Channels 1 and 2, we make a systematic study on the transport properties of the QD-MBS ring. Of particular interest is that there exists a CARassisted ET process in Channel 2, which is different from that in Channel 1. Thus a clear ‘X’ pattern due to the ET and CAR processes appears in the ET, AR, and CAR transport coefficients. Moreover, we study how Channel 2 affects the three transport processes when Channel 1 is tuned in the ET and CAR regimes. It is shown that the transport properties of the ET, AR and CAR processes can be adjusted by tuning the energy level of the QD embedded in Channel 2.Generally, the MBSs can be coupled to the QD system as an embedded part or a side one. In Chapter 4, we investigate the electron transport through a triple QD structure by coupling with two side MBSs. We calculate the conductance of this system as functions of eV with the variation of the QD- MBS couplings, the interdot couplings, and the inter-MBS couplings. It is shown that when the system include two pairs of MBSs, the peaks of the conductance on the sides move away from the zero bias relative to the system including one pair of MBSs. In addition, we analyze the quantum electron transport in the case of asymmetric coupling coefficient when the system include two pairs of MBSs.In the last chapter, we give a brief conclusion of our study.