Polariton Chern Bands in 2D Photonic Crystals Beyond Dirac Cones

Abstract: Polaritons, formed by strong light-matter interactions, open new avenues for studying topological phases, where the spatial and time symmetries can be controlled via the light and matter components, respectively. However, most research on topological polaritons has been confined to hexagonal photonic lattices featuring Dirac cones at large wavenumbers. This restricts key topological properties and device performance, including sub-meV gap sizes that hinder further experimental investigations and future applications of polariton Chern insulator systems. In this study, we move beyond the traditional Dirac cone framework and introduce two alternative band structures in photonic crystals (PhCs) as promising platforms for realizing polariton Chern bands: bands with symmetry-protected bound states in the continuum (BICs) and bands with symmetry-protected degeneracies at the $\Gamma$ points. These band structures are prevalent in various PhC lattices and have features crucial for experimental studies. We show examples of higher Chern number bands, more uniform Berry curvature distributions, and an experimentally feasible system capable of achieving a large topological gap. Our findings show the broad applicability of polariton Chern bands in 2D PhCs, provide design principles for enhancing the functionality and performance of topological photonic devices, opening up exciting possibilities for better understanding and using topological physics.