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

Abstract

We show that the transmission through single and double δ-function potential barriers of strength P = V W b / vF in bilayer graphene is periodic in P with period π. 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 behaviour is found for the conductance. The spectrum of a periodic succession of δ-function barriers (Kronig-Penney model) in bilayer graphene is periodic in P with period 2π. 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 δ-function barriers with P alternating in sign between successive barriers; the corresponding spectrum is periodic in P with period π.

Goos–Hänchen shifts in AA-stacked bilayer graphene superlattices

“…While, in the case of AB-stacked BLG there is no Klein tunneling at normal incidence [3,33]. Now we turn our attention to investigate the basic behaviors of single, double barriers and graphene SLs of AA-stacked BLG for zero gap.…”

Multiband tunneling in trilayer graphene

“…The transport properties of bilayer graphene (BLG), the thinnest multilayer structure, has been extensively studied 2,13,14 . In contrast to monolayer graphene (MLG), it was shown that, within the two band approximation, Klein tunneling does not occur, i.e.…”

Resonant modes in strain-induced graphene superlattices

“…It should also be noted that in the domain within the left cone but outside the second the resonant modes, which are only given by Eq. (8), are characterized by quite narrow lines in the transmission plots.…”

“…(7), in the case N > 1 there exist N − 1 new resonant modes given by Eq. (8). It should also be noted that in the domain within the left cone but outside the second the resonant modes, which are only given by Eq.…”

“…These include low-energy quasiparticles with a Dirac-like spectrum and a linearly vanishing density of states (DOS) at the Fermi level. Evidence of such an unconventional behaviour is to be found in several electronic properties, such as Klein tunneling [5][6][7][8][9] , the optical conductivity [10][11][12] , and the plasmon dispersion relation [13][14][15][16] . These have been predicted to depend quite generally on applied strain 17 , following the earlier suggestion that suitably deformed graphene sheets could be engineered into nanodevices with the desired electron properties 18 .…”