Due to the chiral nature of the Dirac equation, overlying of an electrical
superlattice (SL) can open new Dirac points on the Fermi-surface of the energy
spectrum. These lead to novel low-excitation physical phenomena. A typical
example for such a system is neutral graphene with a symmetrical unidirectional
SL. We show here that in smooth SLs, a semiclassical approximation provides a
good mathematical description for particles. Due to the one-dimensional nature
of the unidirectional potential, a wavefunction description leads to a
generalized Bohr-Sommerfeld quantization condition for the energy eigenvalues.
In order to pave the way for the application of semiclassical methods to two
dimensional SLs in general, we compare these energy eigenvalues with those
obtained from numerical calculations, and with the results from a semiclassical
Gutzwiller trace formula via the beam-splitting technique. Finally, we
calculate ballistic conductivities in general point-symmetric unidirectional
SLs with one electron and one hole region in the fundamental cell showing only
Klein scattering of the semiclassical wavefunctions.Comment: 13 pages, 9 figures, minor corrections, version published in PR
