Extra Dirac points in the energy spectrum for superlattices on single-layer graphene

We investigate the emergence of extra Dirac points in the electronic of a periodically spaced barrier system, i.e., a superlattice, on-layer graphene, using a Dirac-type Hamiltonian. Using square barriers us to find analytic expressions for the occurrence and location of these Dirac points in k-space and for the renormalization of the electron near them in the low-energy range. In the general case of unequal and well widths the new Dirac points move away from the Fermi level and given heights of the potential barriers there is a minimum and maximum width outside of which the new Dirac points disappear. The effect of extra Dirac points on the density of states and on the conductivity is.