Theoretical Study On The Quantum Transport Properties Of Majorana Bound States

Since the Italian particle physicist Ettore Majorana has found the Majorana fermions,this new type of exotic particle has drawn great favor among the physicist.This kind of particle is different from normal fermions,it always appears in pairs and its antiparticle is its own.As it obeys the non Abelian fractional quantum statistics,topological quantum computation is hopefully to be achieved.So far,many theories and experiments have confirmed the presence of Majorana fermions.For example,when a semiconductor with strong spin-orbit coupling is getting close to the s-wave superconductor,a pair of Majorana bound states will occur at the ends of the quantum wires.In this thesis,by adopting the non-equilibrium state Green function method and scattering matrix theory,we analyzed the effects of various mechanisms for Majorana bound state formation systematically and get further knowledge about how the quantum transport properties of the system will be,when Majorana bound state and quantum dot coupled.Finally,we got some meaningful results when we started to use Oreg model and quantum dot ring structure and then analyzed and compared the transport-related physical properties in different theoretical models and system parameters.We are going to introduce our works briefly as follows:First,connect the Majorana bound states of the nano wire with the external circuit in series,make a search on the influence that the superconducting pair potential,the spin-orbit coupling and the uneven magnetic field to the conductance.And then do a survey on the different role that above mentioned field played in the formation of the Majorana bound state.It is found that the inhomogeneity of the magnetic field takes the dominant place in the Majorana bound states,while the inhomogeneity of the superconducting background has relatively small destructive influence on the Majorana bound states.Next,the transport properties of the quantum dot system with the Majorana zero mode is studied.Calculative results show that,when the two electrodes coupled with the quantum pot in the same way,under the extreme limit of zero bias,the local Andreev reflection between electrode and common transport transport has the same value,which makes the zero bias conductance value equal to and happens to be the half of the resonant tunneling conductance values.To explain more specifically,When the Majorana bound state is coupled with the single quantum dot,the zero bias conductance is independent of the energy series and the energy level distribution of the quantum dot.Although there's a change in the conductance value when the Majorana bound state is coupled with the quantum dot molecules,the zero bias conductance is always equal to e2/2h.Therefore,when the quantum dot is used to detect Majorana bound states,it is not affected by the quantum dot property at all.Furthermore,it can be found that the party of the number of dots is the key factor of the formation of persistence current after we've made deep research on the the persistent current in quantum dot chain under the condition that the end of the quantum dots with a Majorana fermions is coupled hybrid quantum dot ring form.The constant current exists when the number of quantum dots is odd,and the current is zero when the quantum number is even.We got diagram of a new ring when we've converted systematic Hamiltonian to the Majorana representation,and we found that only when the quantum number is odd,the hybrid ring can be mapped to a Majorana ring and a Majorana chain,Majorana ring provides a chance for the appearance of continuous current.In the even case,the hybrid ring is a Majorana strand having the same helical direction which leads a restriction of the current.These results can help us to understand the electronic transport properties of mesoscopic systems based on Majorana bound state.