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.

中文翻译：

---

轨道设计的平带模型及三维材料超导的实现

具有平带的电子材料为利用新兴量子现象提供了肥沃的基础。各种二维（2D）系统已经取得了进展，特别是用于研究非常规超导的几何挫败戈薇晶格系统和莫尔超晶格系统。然而，3D 平带系统中的本征超导性尚未有报道。轨道自由度可能会给平带和超导领域带来新的活力。在这里，我们提出了一种轨道设计的 3D 平带模型及其在包含简并的各种材料中的实现$p$-电子，$d$-电子或分子轨道。更重要的是，其中一些 3D 平带材料具有超导性的可能性，例如${\mathrm{K}}_2铅$和${\mathrm{K}}_2双$，通过第一原理计算揭示。有趣的是，这些本质上是多带超导体。我们的研究结果将扩大平带研究的范围，为探索 3D 材料中的相互作用效应和新兴量子相提供线索。