Studies Of The Grid Model Transport Characteristics Composed With The Majorana Fermions

Majorana fermions were proposed and introduced into theoretical physics by Ettore Majorana,and unlike ordinary Dirac fermions,the antiparticles of Majorana fermions are themselves.Because of its high research value in theoretical models,especially Kitaev calculated one dimensional Kitaev chain(imaginary model)which both ends containing the Majorana fermions quasi particles in P wave superconductor theory,more and more researchers work on Majorana fermions.This paper working on the model composed of one-dimensional Kitaev chains,we study the transport characteristics of the grid model composed of ordinary nanowires and Kitaev chains which both ends containing the Majorana fermions,using the non-equilibrium Green’s function.By changing the relationship between the central area and the coupling energy of the left or right electrodes,the central area potential energy and the superconducting pairing potential and the central area transition energy,we find the parameter conditions when containing Majorana fermions near both ends of the Kitaev chain.Secondly,the parallel and interacting two chains are further studied to explore the influence of interchain superconductivity on the transport of the whole model.Then and analyzed the pure Kitaev chain grid model(center of Kitaev chain grid)and hybrid Kitaev grid model(center of Kitaev chain and nanowires)of grid transport properties,at zero bias,the transport mode in pure Kitaev-chain grid model is mainly cross-Andreev reflection,while the transport mode in hybrid Kitaev-chain grid model is mainly local Andreev reflection.With the same parameter relationship,the hybrid Kitaev chain grid model is scattering at the hybrid interface,and the transport image oscillation is more obvious.We subsequently explored the effects of only longitudinal Kitaev or transverse chains on the transport characteristics of pure Kitaev and hybrid Kitaev chain grid models,with particular focus on the variation of local and cross-Andreev reflections.P-wave superconductors are uncommon,but when semiconductor nanowires with strong spin-orbit coupling are coupled to S-wave superconductors under Zeeman energy provided by an external magnetic field,Majorana fermions are also produced at both ends of the semiconductor nanowires.The following work uses the scattering matrix to calculate the differential conductance of one-dimensional long-chain models and grid models on S-wave superconductors.Different magnetic field strength and magnetic field direction are selected in the one-dimensional long-chain model to find the parameter conditions of the zero-bias differential conductance peak.Then under the magnetic field gauge (?)=(-B_zy,-B_xz,-B_yx), the above parameters are selected to study the grid model,fix the width(length)of the center area,and observe the change of zero bias differential conductance with length(width).As the length increases,the zero bias conductance will oscillate;the zero bias conductance will decrease when the width reaches a certain value.In conclusion,when there are Majorana fermions at both ends of the one-dimensional Kitaev chain,at the incident energy is zero can get the following conclusions:(1)the conductance peak exists in the grid model on the S-wave superconductor;(2)the cross-Andreev reflection on the P-wave superconductor dominates the transport,and the local Andreev reflection is suppressed.