  In crystalline systems, charge polarization is related to Zak's phase
determined by bulk band topology. Nontrivial charge polarization induces robust
edge states accompanied with fractional charge. In Su-Schrieffer-Heeger (SSH)
model, it is known that the strong modulation of electron hopping causes
nontrivial charge polarization even in the presence of inversion symmetry.
Here, we consider a bi-atomic honeycomb lattice to introduce such strong
modulation, i.e. A$_3$B sheet. By tuning hopping ratio and onsite potential
difference between A and B atoms, we show that topological phase transition
characterized by Zak's phase occurs. Furthermore, we propose that C$_3$N and
BC$_3$ are the possible realistic materials on the basis of first-principles
calculations. Both of them display topological edge states induced by Zak's
phase without spin-orbital couplings and external fields unlike conventional
topological insulators.
