Nonlocal Quantum Transport In Superconducting Magnetic Silicene Superlattices

Silicene is a two-dimensional graphene-like material composed of a single layer of silicon atoms arranged in a honeycomb structure.Due to its unique buckling structure,silicene has the characteristic of electrical tunability of the energy gap.The ferromagnetism,antiferromagnetism and superconductivity of silicene can be induced experimentally by proximity effects,which makes silicene one of the most promising new materials in silicon atom nanotechnology.In this paper,the nonlocal quantum transport in superconducting magnetic silicene superlattices is studied by using the scattering matrix method.Firstly,we study the crossed Andreev reflection(CAR)and tunneling magnetoresistance(TMR)in silicene-based ferromagnet/superconductor superlattices.The results show that the pure elastic cotunneling(EC)and pure CAR processes can occur simultaneously in silicene band gap with the increase of energy when the number of superconducting strips in the superlattices is odd,while only the pure EC process can occur in silicene band gap when the number of superconducting strips in the superlattices is even.The maximum value of |TMR|increases with the increase of the number of superconducting strips.The TMR is always positive with the increase of energy when the number of superconducting strips in the heterostructures is odd,while it has not only positive but also negative values when the number of superconducting strips in the heterostructures is even.The EC and CAR differential conductances and TMR are symmetric with respect to the staggered potential.Secondly,we study the CAR and TMR in ferromagnet/superconductor double silicene superlattices.The results show that in the multilayer structures,the EC and CAR transmission coefficients show a perfect large peak-to-valley ratio oscillation and a single-peak structure,respectively,while in the superlattice structures,their peaks split into “conjoined twin peaks”,which lead to the increase of the number of peaks.The TMR in the multilayer structures is always positive,while in the superlattice structures it has not only positive but also negative values.As the staggered potential increases,the TMR always remains positive.The EC and CAR transmission coefficients,differential conductances and TMR show quasiperiodic oscillatory behavior with the increase of superconducting barrier height.The EC and CAR transmission coefficients,differential conductances and TMR show rapidly oscillatory behavior with the increase of superconducting barrier width.Compared with multilayer structures,the TMR in superlattice structures reaches its maximum value near superconducting coherence length.Thirdly,we study the nonlocal transport in silicene-based antiferromagnet/superconductor superlattices.The results show that with the increase of energy,the EC transmission coefficient in the multilayer structures appears two linear valleys,and the CAR transmission coefficient appears an obvious single peak structure,while the valleys and peaks of the EC and CAR transmission coefficients in the superlattice structures are split,respectively.The conversion between the pure EC and pure CAR processes can be achieved by changing the electric field.The multilayer structures are favorable for the EC process,while the superlattice structures are favorable for CAR process.Compared with the multilayer structures,the EC and CAR differential conductances decay rapidly to zero with the increase of superconducting barrier width or superconducting energy gap in the superlattice structures.It is hoped that our research will provide theoretical help to the design of silicene electronic devices.