This study investigates the optical response of the square-octagon structure, a two-dimensional carbon allotrope with tetragonal symmetry that exhibits tunable flat bands. Unlike conventional graphene structures, the square-octagon structure features a distinctive geometry characterized by an octagonal framework with rotated square modifications at the corners, belonging to the C₄ point group. The square-octagon structure serves as a promising platform for exploring the interplay between flat band physics, electron correlations, and optical response in two-dimensional Dirac materials. Its tunable flat bands, controlled by next-nearest neighbor hopping (t2), offer a versatile system for studying correlation effects on optical properties. To analyze this system’s electronic and optical properties, we employ the tight-binding model extended with on-site Coulomb repulsion within the Hubbard framework. The electronic band structure is obtained by diagonalizing the Hamiltonian matrix in momentum space, revealing the presence of flat bands whose positions can be adjusted by tuning the next-nearest neighbor hopping parameters. Using Kubo linear response theory, we compute the frequency-dependent absorption coefficient, examining how flat bands influence the material’s interaction with electromagnetic radiation. Additionally, we calculate the transmissivity and reflectivity coefficients to further characterize the optical response of this structure.
