Density of states in finite graphene superlattices

We have derived a formula for the density of states 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 along the SL-axis. Using that... [ view full abstract ]

We have derived a formula for the density of states 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 along the SL-axis. Using that formula, it was shown that density of states 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, the inverse of the group delay velocity is proportional to the transmission coefficient, which allows us to establish a certain correlation between the properties of the density of states and those of the Landauer conductance of the N-period SL. Certainly, the Landauer conductance exhibits a peak structure as a function of E, with local dips located at the same energies as those of the density of states. The same behavior was observed for the group delay velocity-dependence of the Landauer conductance with E=0, which is very similar to that of the density of states. When N increases, the peak positions of both the Landauer conductance and the density of states tend to be located at those values of group delay velocity where new Dirac points appear.