RESUMEN
Recently, there has been growing interest in the field of flat-band physics due to its attractive properties and wide range of practical applications. In this study, we introduce two novel two-dimensional monolayers, namely B3C11O6 and B3C15O6, which exhibit a flat band near the Fermi level. These monolayers have been found to be energetically favorable, dynamically stable, and thermodynamically stable based on formation energies, phonon spectra, and molecular dynamics simulations. The nearly flat band (NFB) in B3C11O6 arises from the extended kagome sublattice of carbon atoms. Due to the strong interaction between carbon atoms beyond their nearest neighbors, the bandwidth of the initial flat band is extended to approximately 0.5 eV. Nevertheless, there is still a prominent peak in the density of states near the Fermi level. On the other hand, the NFB in B3C15O6 originates from the localized states of the carbon five-ring structure, which forms a distorted kagome lattice. The presence and characteristics of the NFB strongly depend on the interactions between next-nearest neighbors. Interestingly, the partially occupied NFB in B3C11O6 leads to spin splitting, resulting in a transformation of the system into a ferromagnetic metal. Our research not only presents two types of lattices capable of hosting flat bands or NFBs, but also provides two monolayers that can be employed to investigate various intriguing quantum phases.