Tunneling through finite graphene superlattices: resonance splitting effect.

An exact expression of the transmission probability through a finite graphene superlattice with an arbitrary number of potential barriers n is derived in two cases of the periodic potential: rectangular electric potential and δ-function magnetic potential. Obtained transmission probabilities show two types of resonance energy: barrier-induced resonance energies unchanged as n varies and well-induced resonance energies that have undergone the (n - 1)-fold splitting as n increases. Supported by numerical calculations for various types of graphene superlattices, these analytical findings are assumed to be equally applied to all of the finite graphene superlattices regardless of their potential nature (electric or magnetic) and potential barrier shapes.