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