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

## TL;DR

This paper explores topological edge states in A3B monolayers induced by Zak's phase, demonstrating phase transitions and edge states in realistic materials like C3N and BC3 through theoretical and first-principles analysis.

## Contribution

It introduces a new class of topological phases in A3B monolayers driven by Zak's phase, supported by first-principles calculations of realistic materials.

## Key findings

- Topological phase transition occurs with tuning hopping ratio and onsite potential.
- C3N and BC3 exhibit topological edge states induced by Zak's phase.
- Edge states appear without spin-orbit coupling or external fields.

## Abstract

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.