Dwell time, Hartman effect and transport properties in a ferromagnetic phosphorene monolayer

In this paper, spin-dependent dwell time, spin Hartman effect and spin-dependent conductance were theoretically investigated through a rectangular barrier in the presence of an exchange field by depositing a ferromagnetic insulator on the phosphorene layer in the barrier region. The existence of the spin Hartman effect was shown for all energies (energies lower than barrier height) and all incident angles in phosphorene. We also compared our results of the dwell time in the phosphorene structure with similar research performed on graphene. We reported a significant difference between the tunneling time values of incident quasiparticles with spin-up and spin-down. We found that the barrier was almost transparent for incident quasiparticles with a wide range of incident angles and energies higher than the barrier height in phosphorene. We also found that the maximum spin-dependent transmission probability for energies higher than barrier height does not necessarily occur in the zero incident angle. In addition, we showed that the spin conductance for energies higher (lower) than barrier height fluctuates (decays) in terms of barrier thickness. We discovered that, in contrast to graphene, the Klein paradox does not occur in the normal incident in the phosphorene structure. Furthermore, the results demonstrated the achievement of good total conductance at certain thicknesses of the barrier for energies higher than the barrier height. This study could serve as a basis for investigations of the basic physics of tunneling mechanisms and also for using phosphorene as a spin polarizer in designing nanoelectronic devices.