Spin-dependent group delay time and Hartman effect in ferromagnetic bilayer graphene superlattice

We theoretically study the spin-dependent group delay time through ferromagnetic bilayer graphene superlattice in the absence and presence of the bandgap. It is found that the group delay time depends on the spin degree of freedom and exhibits an oscillatory behavior with respect to the Fermi energy and barrier width. Furthermore, in the absence of the bandgap, the superluminal or Hartman effect exists only for the normal angle of incidence. Moreover, when bandgap value is large enough [Formula: see text], the Hartman effect can be observed for all angles of incidence. These results are contrary to the observed behavior for monolayer graphene superlattice.