Transport Properties In Parallel Mesoscopic Circuits Coupled With Majorana Bound States

In recent years,many research groups have conducted a great deal of researches on the transport properties of Majorana fermions and superconductors heterogeneous junctions,due to their unique non-Abelian statistics and their applications in topological quantum information computing.Cross-Andreev reflections in the fringe state of Majorana fermions were found to be suppressed and so on.At the same time,in condensed matter physics,Majorana bound states can be obtained at both ends by applying a magnetic field and an s-wave superconductor or a semiconductor quantum wire.The bound states are closely linked to electron spin-orbit coupling,superconductivity,Fano Effects,etc.and then attract more and more researchers in the field of quantum computers.With the discovery of Majorana fermions,Majorana bound states have become the research focus of low-dimensional semiconductor structures.Therefore,it is more important to explore the transport characteristics of Majorana bound states systems.In this paper,based on the non-equilibrium Green’s function method and the scattering matrix method,we first theoretically study the electron transport properties of a parallel coupled quantum system with multiple quantum dots,in which the terminal point of the one-dimensional quantum dots chain is placed in the arms of the Aharonov-Bohm(AB)interferometer.We find that in the odd(even)dots structure,all their even(odd)molecular states have a chance of decoupling from the lead,In this process,the antiresonance is consistent with the odd(even)number of the characteristic energy of the molecule without the terminal points.Next,antiresonance and decoupling phenomenas still coexist in the quantum transmission when Majorana zero mode is laterally coupled to the termination points.Then we further design three Majorana-Fano interferometers to study the transport properties of the Majorana bound states in mesoscopic circuits.The cross Andreev reflectance and local Andreev reflectance conductance expressions of the three interferometers are calculated and the corresponding numerical calculations are carried out.During studying the effect of local magnetic flux on transport properties,we find that the cross Andreev reflections and local Andreev reflections of each model driven by the Majorana bound states are mutually suppressed in low-energy excited states.We conclude that there are also some other unique properties of each conductivity spectra,mainly reflected in the conductance at the zero bias point.In addition,we also found that the Andreev reflectivity of the system can be effectively adjusted by adjusting the interactional coefficient between the Majorana bound states and the coupling coefficient between the Maj orana bound states and the electrode.So far,the purpose of our exploration is basically fulfilled.For the electron transport behavior of the AB ring system containing the Majorana bound states,the results help to further understand the special influence of Majorana bound states on the electron transport through the quantum dot systems and lay a new foundation for topological quantum computation.