  We studied the Klein paradox in zigzag (ZNR) and anti-zigzag (AZNR) graphene
nanoribbons. Due to the fact that ZNR (the number of lattice sites across the
nanoribbon (N is even) and AZNR (N is odd) configurations are indistinguishable
when treated by the Dirac equation, we supplemented the model with a
pseudo-parity operator whose eigenvalues correctly depend on the sublattice
wavefunctions for the number of carbon atoms across the ribbon, in agreement
with the tight-binding model. We have shown that the Klein tunneling in zigzag
nanoribbons is related to conservation of the pseudo-parity rather than
pseudo-spin in infinite graphene. The perfect transmission in the case of
head-on incidence is replaced by perfect transmission at the center of the
ribbon and the chirality is interpreted as the projection of the pseudo-parity
on momentum at different corners of the Brillouin zone.
