Quantum Transport In A Silicene-based Superconducting Double Barrier Heterojunction With Ferromagnetic Electrodes

Silicene,a two-dimensional graphene-like material formed by silicon atoms distributed in a honeycomb lattice,has attracted a great deal of attention from both experimental and theoretical points of view.In this paper,we mainly study quantum transport in a silicene-based superconducting double barrier(SDB)heterojunction with ferromagnetic electrodes(F).The main results obtained are listed below:Firstly,we investigate theoretically the local and nonlocal transports in a silicene-based superconducting double barrier tunnel junction with two ferromagnetic electrodes(F/SDB/F tunnel junction).Using transfer matrix method,the crossed Andreev reflection(CAR),local and nonlocal differential conductances are numerically calculated.We find that the pure elastic cotunneling(EC)in the parallel configuration of magnetizations of the two ferromagnetic electrodes and the pure CAR process in the antiparallel configuration of magnetizations of the two ferromagnetic electrodes can be obtained by increasing the incident energy,and the region widths of the pure EC and pure CAR can be tuned by the exchange splitting energy.The CAR differential conductance exhibits a plateau in low electric field region for the antiparallel configuration of magnetizations of the two ferromagnetic electrodes by increasing the external electric field.The nonlocal differential conductance decreases monotonically with increasing superconducting gap,and the nonlocal transport processes are suppressed when the superconducting gap is large.We also find that the CAR,local and nonlocal differential conductances show periodic oscillations with increasing the insulating barrier potential and superconducting barrier potential,along with typical quasiperiodic oscillations as the middle insulator region width increases.Secondly,we investigate theoretically the local and nonlocal transports in a silicene-based superconducting double barrier ferromagnetic(SDBF)double junction.Using transfer matrix method,the CAR,local and nonlocal differential conductances are numerically calculated.We find that the pure EC in both the parallel configuration and the antiparallel configuration of magnetizations of adjacent ferromagnets can be obtained by increasing the incident energy,and the region width of the pure EC is robust against the middle ferromagnetic exchange splitting energy.The distributions of the CAR,local and nonlocal differential conductances are symmetric with respect to the external electric field.As the superconducting gap increases,the CAR differential conductance initially increases and then begins to decreases,the local differential conductance shows opposite behavior compared to the CAR differential conductance,and the nonlocal differential conductance decreases monotonically.And the CAR,local and nonlocal differential conductances in the parallel configuration of magnetizations of adjacent ferromagnets show opposite dependence on the middle ferromagnetic exchange splitting energy compared to those in the antiparallel configuration of magnetizations of adjacent ferromagnets.We also find that the CAR,local and nonlocal differential conductances show periodic oscillations with increasing the superconducting barrier potential and insulating barrier potential,and the peaks of the local and nonlocal differential conductances in the parallel configuration of magnetizations of adjacent ferromagnets exhibit a splitting behavior as the middle ferromagnetic exchange splitting energy increases.Moreover,the CAR,local and nonlocal differential conductances exhibit the typical quasiperiodic oscillations as functions of the middle ferromagnetic region width.