  We theoretically study the 2D Su-Schrieffer-Heeger model in the context of
Floquet topological insulators (FTIs). FTIs are systems which undergo
topological phase transitions, governed by Chern numbers, as a result of time
reversal symmetry (TRS) breaking by a time periodic process. In our proposed
model, the condition of TRS breaking is achieved by circularly polarized light
irradiation. We analytically show that TRS breaking is forbidden in the absence
of second order neighbors hopping. In the absence of light irradiation, we
identify a symmetry-protected degeneracy and prove the appearance of a flat
band along a specific direction in the momentum space. Furthermore, we employ a
novel method to show that the four unit cell atoms, in the absence of
irradiation, can be interpreted as conserved spin states. With the breaking of
TRS via light irradiation, these spin states are no longer conserved, leading
to the emergence of chiral edge states. We also show how the interplay between
the TRS breaking and dimerization leads to a complex phase diagram. The
validity of our findings is substantiated through Chern numbers, spectral
properties, localization of chiral edge states and simulations of quantum Hall
transport. Our model is suitable not only for condensed matter (materials), but
also for cold gases trapped in optical lattices or electric circuits.
