Topological Edge States Induced by Zak's Phase in A3B Monolayers

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.