Laser-assisted tunneling and Hartman effect in graphene under scalar potential and exchange fields

We study the tunneling effect of Dirac fermions in a graphene sheet by introducing a potential barrier in a region of width $D$ exposed to laser field. This sheet is placed on a boron nitride/ferromagnetic substrate such as cobalt or nickel. By using the Floquet theory, we determine the solutions of the energy spectrum. We calculate the transmission and reflection coefficients by applying the boundary conditions along with the transfer matrix method. These coefficients help determine their probabilities by current densities and group delay times by their phases. We numerically show that the laser field plays a crucial role in this structure, as it completely suppresses Klein tunneling compared to the case without laser. Furthermore, in contrast to the Hartman effect, the group delay time becomes dependent on the barrier width with the appearance of additional peaks. This suggests that fermion-field interactions cause additional delays within the barrier and also help to reduce spin coupling. Adding BN layers increases the interval of transmission suppression and completely eliminates coupling after the addition of three BN layers. Total reflection is observed for incident fermions with an angle less than $-1$ or greater than one.