Electronic materials with a flat-band provide a fertile foundation for exploiting emerging quantum phenomena. Progress has been made in various two-dimensional (2D) systems, especially in a geometric frustrated kagome lattice system and a moire superlattice system for the study of unconventional superconductivity. However, intrinsic superconductivity has not yet been reported in 3D flat-band systems. The orbital degree of freedom might bring new vitality into the field of flat bands and superconductivity. Here, we propose an orbital-designed 3D flat-band model and its realization in various materials containing degenerate $p$-electrons, $d$-electrons, or molecular orbitals. More importantly, the possibility of superconductivity in some of these 3D flat-band materials, e.g., ${\mathrm{K}}_2\mathrm{Pb}$ and ${\mathrm{K}}_2\mathrm{Bi}$, is revealed via first-principles calculations. Interestingly, these are intrinsically multiband superconductors. Our findings would expand the scope of flat-band studies, shedding light on the exploration of interacting effects and emerging quantum phases in 3D materials.

• Received 17 September 2023
• Accepted 25 April 2024

DOI:https://doi.org/10.1103/PhysRevB.109.L180504