Graphene superlattices: Effect of finite size on the density of states and conductance

We have derived a formula for the density of states ρ N ( E ) of a N ‐period graphene superlattice (SL), which is given as an integral over the inverse of the absolute value of the group delay velocity v x along the SL‐axis. Using that formula, it was shown that ρ N ( E ) exhibits essentially the same structure for all values of N ≥ 5 . It was found that for E < 0 , the effects of finite crystal size modify dramatically the density of states of the corresponding infinite SL, whereas for E > 0 and N ≥ 5 , it is only slightly modified. According to our results, 1 / v x is proportional to the transmission coefficient, which allows us to establish a certain correlation between the properties of ρ N ( E ) and those of the Landauer conductance G N ( E ) of the N ‐period SL. Certainly, G N ( E ) exhibits a peak structure as a function of E , with local dips located at the same energies as those of ρ N ( E ) . The same behavior was observed for the V ‐dependence of G N ( E ) with E = 0 , which is very similar to that of ρ N ( 0 ) . When N increases, the peak positions of both G N ( 0 ) and ρ N ( 0 ) tend to be located at those values of V where new Dirac points appear.