# Emergence of photo-induced multiple topological phases on square octagon lattice

## TL;DR

This paper demonstrates how circularly polarized light induces multiple topological phases in a square octagon lattice, revealing phase transitions and topological properties through Floquet theory and Chern number analysis.

## Contribution

It introduces a model showing light-induced topological phase transitions on a square octagon lattice, including the emergence of Chern insulator and semimetal phases.

## Key findings

- Multiple topological phases emerge with light amplitude variation.
- Topological phase transitions occur upon changing hopping strengths.
- Chern numbers and edge states confirm topological properties.

## Abstract

In this study, a tight-binding model on square octagon lattice with nearest-neighbour and next-nearest-neighbour hoppings is considered. The system is topologically trivial although it exhibits quadratic band-touching points in its band-structure. It is shown that the system drives towards topologically non-trivial phases as soon as it is exposed to monochromatic circularly polarized light. Multiple topological phases are found to emerge with the variation of amplitude of light. An effective time-independent Hamiltonian of the system is obtained following the Floquet-Bloch formulation. Quasi-energy band-structures along with definite values of Chern numbers for respective bands are obtained. Characterization of topological phases are made in terms of band structure and Chern numbers. In addition, Hall conductance and topologically protected chiral edge states are obtained to explain the topological properties. Density of states is obtained in every case. The system undergoes a series of topological phase transitions among various topological phases upon variations of both amplitude of light and hopping strengths. It exhibits Chern insulating and Chern semimetallic phases depending on the values of lattice filling.