Prediction of the lightest three-dimensional diamond-like fullerene phase with orbital-coupling-tunable pseudo-Dirac states and flat band states

The discovery of novel carbon allotropes---from fullerenes and nanotubes to graphene---has greatly advanced contemporary materials research. Beyond conventional atomic crystals, superatomic solids provide an attractive platform for exploring structure-property relationships arising from their unique hierarchical architectures. Here, using state-of-the-art first-principles calculations, we propose a three-dimensional (3D) diamond-like fullerene (C₆₀) phase, dubbed fullerdiamond (FLD), constructed by substituting each carbon atom in diamond with a C₆₀ superatom, where each C₆₀ covalently connects to its four neighbors via four 66/66 [2+2] cycloadditions. Our calculations reveal that FLD is structurally stable, with the lowest density (1.098 g/cm³) among diamond-type structures and anisotropic Young's moduli of 50.91~85.35 GPa. Its electronic structure exhibits a sizable indirect band gap of 1.83 eV and two distinctive features: (i) an accidental pseudo-Dirac cone ({~}57 meV gap) in the conduction band arising from antibonding coupling between LUMO states of neighboring C₆₀ superatoms, and (ii) a narrow flat band ({~}104 meV) in the valence band. Moreover, a tensile strain of {~}3% along the [100] direction weakens the antibonding orbital coupling between neighboring C₆₀ superatoms through elongation of the inter-cage [2+2] cycloaddition bonds, reducing the accidental pseudo-Dirac gap to {~}4 meV and narrowing the flat band width to {~}88 meV. This strain-tunable electronic behavior---arising from the sensitivity of inter-C₆₀ orbital coupling to lattice deformation---establishes a conceptual bridge between fullerene molecular physics and diamond-like 3D superatomic solid physics. Our findings highlight FLD as a promising platform for tuning electronic and optical properties in lightweight carbon-based materials.