  We present a two-dimensional (2D) lattice model that exhibits a nontrivial
topological phase in the absence of the Berry curvature. Instead, the Berry
connection provides the topological nontrivial phase in the model, whose
integration over the momentum space, the so-called 2D Zak phase, yields a
fractional wave polarization in each direction. These fractional wave
polarizations manifest themselves as degenerated edge states with opposite
parities in the model.
