Study On Transport Properties Of Faye Ferrari Fermi System

The generation/detection of Majorana fermions (MF) in condensed matter systems is a hot topics.In this paper, we mainly focus on the transport properties of coupled Majorana fermion system, including Fano resonance of the quantum dot-topological superconducting nanowire-quantun dot system, Aharonov Bohm effect of the QD-TSNW-QD system, and Andreev reflection of the coupled Majorana fermions.Firstly, we systematically study the Fano effect of the QD-TSNW-QD system. When the energy levels of the two quantum dots are set align with each other, the Andreev behaviour in transport process is completely supressed, the electron teleportation spectra display the properties of Fano resonance. By tuning the coupling strength of the Majorana fermions and the energy level of the two quantum dots, one can manage the component of the three eigenstates of the middle system. We discuss three situations which can be exactly solved, and give the methods of modulation Fano peak asymmetry and position quantitatively. Using the relationship between the Fano factor and coupling strength of MFs, one can design a theoretical scheme of measuring nanowire length by conductance spectroscopy.Then we qualitative analysis the influence of magnetic flux on transport properties of the QD-TSNW-QD which is parallel coupled with two electrodes system. When the energy levels of the two quantum dots is aligned and when there is no interaction between Majorana bound states, one can achieve interconversion between electron teleportation mechanism and local Andreev reflection mechanism by adjusting the flux. The period of the conductance oscillation with flux for three transport mechanisms is 2π; when the interaction between Majorana bound states is turned on, the whole system period of the conductance with flux is 4%, the suppression of the three transport mechanism by flux is weakened. Besides, the presence of the Andreev reflection makes Fano resonance become more complex.Lastly, we discuss in detail the Andreev reflection of the system of the coupled Majorana fermions. the zero bias Andreev reflection conductance is decided by the parity of Majorana fermions’ number. We give the recurrence relation between anti-resonance and the resonance on the conductance spectrum. When there are a number of the Majorana fermions, in the energy scale of Andreev reflection conductivity oscillates with the electrode voltage vigorously, demonstrating the characteristics of the oscillation band. Andreev reflection of the coupled Majorana fermions with is similar to transmission spectrum of the side coupled quantum dot chain, Andreev reflection spectrum of the coupled Majorana fermions can be inferred by the transmission conductance of side coupled quantum dot system.