Orbital-designed flat-band model and realization of superconductivity in three-dimensional materials

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., K2Pb and K2Bi, 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.