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 delta-function potential barriers of strength P =VW(b)/(h) over barv(F) in bilayer graphene is periodic in P with period pi. 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 delta-function barriers (Kronig-Penney model) in bilayer graphene is periodic in P with period 2 pi. For P smaller than a critical value P(c), the spectrum exhibits two Dirac points while for P larger than P(c) an energy gap opens. These results are extended to the case of a superlattice of delta-function barriers with P alternating in sign between successive barriers; the corresponding spectrum is periodic in P with period pi.