Resonant peak splitting in finite periodic superlattices with an unit cell of two barriers and two wells on monolayer graphene

The general expressions for transmission probability and resonant peaks in one-dimensional N-periods graphene superlattice with unit cell of two barriers and two wells are analytically derived, and two types of resonant peaks are obtained: (1) the periodicity induced resonant peaks splitting of (N − 1)-fold as N increases; and (2) the resonant peak through a unit cell unchanged as N varies. As the two-barriers in unit cell become asymmetric, the resonance transmission probability of unit cell becomes imperfect (T₁ < 1), which drops quickly with the unit asymmetry increases. Thus, the unit cell related resonant peak could only be observed in superlattices with less unit cell asymmetry of a few of period numbers. With the period increases, the unit related resonant peak disappears and only periodicity induced (N − 1)-fold splitting remains. The splitting rule is further confirmed by the conductance and noise versus the incident energy and the misunderstandings in publication domain is cleared up.