An indispensable ingredient for pair density wave (PDW) superconductivity is the presence of an attractive pairing interaction at finite momentum. Here, we show how this condition can be met with straightforward electron-density interactions in multiband systems. The electron-density interaction, when projected to the band basis, acquires form factors with nontrivial momentum dependence and thereby exhibits a potential tendency to a finite-momentum pairing instability. By applying a mean field analysis to two simple multiband models, the checkerboard lattice and three-band Hubbard model, we find that PDW order can indeed become the leading instability if a strong nearest-neighbor attraction is present. Moreover, the condition for the transition from a uniform superconductor to a PDW superconductor is shown via a simple quantum geometric argument.

中文翻译：

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多频带系统中的对密度波阶


对密度波（PDW）超导性的一个不可或缺的因素是在有限动量下存在有吸引力的配对相互作用。在这里，我们展示了如何在多带系统中通过简单的电子密度相互作用来满足这个条件。当投影到能带基础时，电子密度相互作用获得具有非平凡动量依赖性的形状因子，从而表现出有限动量配对不稳定性的潜在趋势。通过对两个简单的多带模型（棋盘格和三带 Hubbard 模型）应用平均场分析，我们发现如果存在强的最近邻吸引力，PDW 阶确实可以成为主要的不稳定性。此外，通过简单的量子几何论证显示了从均匀超导体到PDW超导体的转变条件。