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 (${\mathrm{C}}_{60}$) phase, dubbed fullerdiamond (FLD), constructed by substituting each carbon atom in diamond with a ${\mathrm{C}}_{60}$ superatom, where each ${\mathrm{C}}_{60}$ 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 $\mathrm{g}/{\mathrm{cm}}^{3}$) among diamond-type structures and anisotropic Young's moduli of $50.91\ensuremath{\sim}85.35$ GPa. Its electronic structure exhibits a sizable indirect band gap of 1.83 eV and two distinctive features: (i) an accidental pseudo-Dirac cone (\ensuremath{\sim}57 meV gap) in the conduction band arising from antibonding coupling between LUMO states of neighboring ${\mathrm{C}}_{60}$ superatoms, and (ii) a narrow flat band (\ensuremath{\sim}104 meV) in the valence band. Moreover, a tensile strain of \ensuremath{\sim}3% along the [100] direction weakens the antibonding orbital coupling between neighboring ${\mathrm{C}}_{60}$ superatoms through elongation of the inter-cage [2+2] cycloaddition bonds, reducing the accidental pseudo-Dirac gap to \ensuremath{\sim}4 meV and narrowing the flat band width to \ensuremath{\sim}88 meV. This strain-tunable electronic behavior---arising from the sensitivity of inter-${\mathrm{C}}_{60}$ 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.