  Photonic pseudospin-1/2 systems, which exhibit Dirac cone dispersion at
Brillouin zone corners in analogy to graphene, have been extensively studied in
recent years. However, it is known that a linear band crossing of two bands
cannot emerge at the center of Brillouin zone in a two-dimensional photonic
system respecting time reversal symmetry. Using a square lattice of elliptical
magneto-optical cylinders, we constructed an unpaired Dirac point at the
Brillouin zone center as the intersection of the second and third bands
corresponding to the monopole and dipole excitations. Effective medium theory
can be applied to the two linearly crossed bands with the effective
constitutive parameters numerically calculated using the boundary effective
medium approach. It is shown that only the effective permittivity approaches
zero while the determinant of the nonzero effective permeability vanishes at
the Dirac point frequency, showing a different behavior from the double-zero
index metamaterials obtained from the pseudospin-1 triply degenerate points for
time reversal symmetric systems. Exotic phenomena, such as the Klein tunneling
and Zitterbewegung, in the pseudospin-1/2 system can be well understood from
the effective medium description. When the Dirac point is lifted, the edge
state dispersion near the $\Gamma$ point can be accurately predicted by the
effective constitutive parameters. We also further realized magneto-optical
complex conjugate metamaterials for a wide frequency range by introducing a
particular type of non-Hermittian perturbations which make the two linear bands
coalescence to form exceptional points at the real frequency.
