Electrons with large kinetic energy have a superconducting instability for infinitesimal attractive interactions. Quenching the kinetic energy and creating a flat band renders an infinitesimal repulsive interaction the relevant perturbation. Thus, flat-band systems are an ideal platform to study the competition of superconductivity and magnetism and their possible coexistence. Recent advances in the field of twisted bilayer graphene highlight this in the context of two-dimensional materials. Two dimensions, however, put severe restrictions on the stability of the low-temperature phases due to enhanced fluctuations. Only three-dimensional flat bands can solve the conundrum of combining the exotic flat-band phases with stable order existing at high temperatures. Here, we present a way to generate such flat bands through strain engineering in topological nodal-line semimetals. We present analytical and numerical evidence for this scenario and study the competition of the arising superconducting and magnetic orders as a function of externally controlled parameters. We show that the order parameter is rigid because the three-dimensional quantum geometry of the Bloch wave functions leads to a large superfluid stiffness in all three directions. Using density-functional theory and numerical tight-binding calculations, we further apply our theory to strained rhombohedral graphite and CaAgP materials.

中文翻译：

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在节线半金属中设计三维平面带

具有大动能的电子对于无穷小的吸引力相互作用具有超导不稳定性。淬灭动能并产生平坦带使相关扰动产生无穷小的排斥相互作用。因此，平带系统是研究超导和磁性的竞争及其可能共存的理想平台。扭曲双层石墨烯领域的最新进展在二维材料的背景下突出了这一点。然而，由于波动的增加，二维对低温相的稳定性施加了严格的限制。只有三维平带才能解决将奇异的平带相与高温下存在的稳定有序相结合的难题。这里，我们提出了一种通过拓扑节点线半金属中的应变工程生成这种平坦带的方法。我们为这种情况提供了分析和数值证据，并研究了作为外部控制参数函数的超导和磁阶的竞争。我们表明阶参数是刚性的，因为布洛赫波函数的三维量子几何在所有三个方向上都导致了很大的超流体刚度。使用密度泛函理论和数值紧束缚计算，我们进一步将我们的理论应用于应变菱形石墨和 CaAgP 材料。我们表明阶参数是刚性的，因为布洛赫波函数的三维量子几何在所有三个方向上都导致了很大的超流体刚度。使用密度泛函理论和数值紧束缚计算，我们进一步将我们的理论应用于应变菱形石墨和 CaAgP 材料。我们表明阶参数是刚性的，因为布洛赫波函数的三维量子几何在所有三个方向上都导致了很大的超流体刚度。使用密度泛函理论和数值紧束缚计算，我们进一步将我们的理论应用于应变菱形石墨和 CaAgP 材料。