  Topological flat bands (TFBs) are increasingly recognized as an important
paradigm to study topological effects in the context of strong correlation
physics. As a representative example, recently it has been theoretically
proposed that the topological non-triviality offers a unique contribution to
flat-band superconductivity, which can potentially lead to a higher critical
temperature of superconductivity phase transition. Nevertheless, the
topological effects within flat bands in bosonic systems, specifically in the
context of Bose-Einstein condensation (BEC), are less explored. It has been
shown theoretically that non-trivial topological and geometric properties will
also have a significant influence in bosonic condensates as well. However,
potential experimental realizations have not been extensively studied yet. In
this work, we introduce a simple photonic lattice from coupled Kagome and
triangular lattices designed based on topological quantum chemistry theory,
which supports topologically nontrivial quasi-flat bands. Besides band
representation analysis, the non-triviality of these quasi-flat bands is also
confirmed by Wilson loop spectra which exhibit winding features. We further
discuss the corresponding experimental realization in a microcavity array for
future study supporting the potential extension to condensed
exciton-polaritons. Notably, we showed that the inevitable in-plane
longitudinal-transverse polarization splitting in optical microcavities will
not hinder the construction of topological quasi-flat bands. This work acts as
an initial step to experimentally explore the physical consequence of
non-trivial topology and quantum geometry in quasi-flat bands in bosonic
systems, offering potential channels for its direct observation.
