Cyclacene-derived carbon lattices with distorted hexagonal tiling and in-plane π-orbitals: coexistence of flat and Dirac bands.

The discovery of nanomaterials with unique electronic band structures, such as flat bands, has drawn significant interest for enabling novel physical phenomena and advanced technological applications. Kagome lattices, characterized by corner-sharing triangles, are a notable class of materials featuring the coexistence of flat and Dirac bands. This study investigates a new class of carbon lattices derived from cyclacene molecules (cyc-CL), featuring a distorted hexagonal tiling. In these two-layer carbon structures with hydrogen-saturated bonds, π orbitals lie parallel to the layers, unlike typical 2D carbon materials. Using first-principles DFT calculations, we analyze three variants (6-cyc-CL, 12-cyc-CL, and 18-cyc-CL), examining band gaps, density of states (DOS), and orbital contributions. Cyc-CL systems exhibit tunable band gaps, flat and Dirac bands near the Fermi level, and dominant π orbitals from p _x and p _y states. These results highlight cyc-CL's potential for studying quantum phenomena and enabling nanotechnology applications.