Kronig-Penney model on bilayer graphene: Spectrum and transmission periodic in the strength of the barriers

We show that the transmission through single and double -function potential barriers of strength P =VWb / vF in bilayer graphene is periodic in P with period . For a certain range of P values we find states that are bound to the potential barrier and that run along the potential barrier. Similar periodic behavior is found for the conductance. The spectrum of a periodic succession of -function barriers Kronig-Penney model in bilayer graphene is periodic in P with period 2 . For P smaller than a critical value Pc, the spectrum exhibits two Dirac points while for P larger than Pc an energy gap opens. These results are extended to the case of a superlattice of -function barriers with P alternating in sign between successive barriers; the corresponding spectrum is periodic in P with period .