| With the discovery of Majorana fermions by theoretical physicist Ettore Majorana. Research on this strange particle in physics community are never stopped. The reason not only the antiparticle is itself, no mass, no charge, no spin, and stay in a zero energy state, but also because such particles obey non-Abelian quantum statistics. Topological quantum computing can take to build topological quantum computer. In recent years, the research of Majorana fermions have a huge breakthrough in the field of solid state physics. We can apply a magnetic field and s-wave superconductors to the semiconductor quantum wires and the Majorana bound state will appear at the ends of the quantum wires. It provides a new way for people to recognize and manipulate Majorana bound states. Meanwhile, as a basic research, the discussion about the Majorana bound state transport properties of the system is necessary.In this paper, we used the theory of non-equilibrium Green’s function method and scattering matrix. We studied the effects of the Majorana bound states on transport properties in two kinds of quantum dot structures systematically, i.e., a T-shaped quantum-dot structure and a T-shaped double quantum dot structure. Next we analyze and compare the transport-related physical properties in different theoretical models and system parameters, such as conductivity and noise value. Finally, we get some meaningful results. We introduce our works briefly from two aspects as follows:Firstly, we establish a T-shaped quantum-dot structure and obtain some results through calculating the conductance in the case of appropriate structure parameters. It is found that if the Majorana bound states is not coupled with quantum dots, the conductance spectra at zero bias limit is differentiated by the number of coupled quantum dots. Namely, when the number of coupled quantum dot is odd, the conductance at zero bias limit shows a resonance peak whose value is e2/h.If the number of coupled quantum dot is even, the conductance at zero bias limit will be antiresonant. However, if the Majorana bound states is introduced to couple with quantum dots, the odd-even effect of the zero-bias conductance will disappear. Meanwhile, the conductance value becomes equal to e2/2h at the zero-bias limit,which is independent of the number of the quantum dots and the structure parameters. The result completely change the parity effect in the transport spectra of the T-shaped quantum dots. Undoubtedly, this new phenomenon can help to understand the modulation of MBS on the mesoscopic circuit transport behavior and can also help to complete the MBS detection.Secondly, we investigate the Andreev reflection in a T-shaped DQD structure induced by MBSs. We find a well-defined insulating band in the Andreev conductance spectrum in the low-bias region by evaluating the Andreev conductance. Next, by using the unitary transformation, we transform the T-shaped quantum dot structure into a model in which three T-shaped quantum dots are coupled serially. We discusse the effect of structural parameters on the insulating band in detail by analyzing the transport properties of such a structure. As a result, it is found that three antiresonance points induced by the three T-shaped quantum dots lead to the emergence of the insulating band. Additionally, the Fano factor has been presented, which can also reflect the characteristics of insulating band. We believe that all the results can help to understand the nontrival role of the MBSs in manipulating the Andreev reflection. |
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