Simple realization of a fragile topological lattice with quasi flat-bands in a microcavity array

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.