Topological Flat Bands in 2D Optical Plasmonic Valley Photonic Crystals

Topological insulators and flat bands have recently emerged as pivotal subjects in the field of condensed matter physics. Due to the non-dispersive nature of flat bands, energy is no longer directly related to momentum, being confined within the structure. While ideal flat bands within the tight-binding model have been extensively studied, quasi flat bands influenced by omnipresent perturbations are accepted in practical applications. The amalgamation of flat bands with topology, facilitated through symmetry analysis, allows for the facile realization of topological flat bands without necessitating complex superlattice analyses, while preserving time-reversal symmetry. Recent research has extensively explored flat bands across diverse systems. In optics, the phenomena and applications stemming from flat bands in light transmission have been thoroughly investigated. The fusion of topology and flat bands introduces new dimensions to the study of condensed matter physics. Leveraging internal symmetries or designed couplings, flat bands find realization in various systems, including kagome lattices, Chern topological insulators, and twisted bilayer systems. This paper initiates by presenting the latest research advancements concerning flat bands in diverse systems. The second section provides an introduction to the theory of topological band structures. This involves research on tight-binding models and 2D optical plasmonic valley photonic crystals, exploring their band structure and topological properties. The third section delves into topological states within different nontrivial band gaps, encompassing edge and corner states. Finally, in the fourth section, we offer a prospective outlook on the future developments of employing topological flat bands across different platform and their application in highly integrated devices.