AI 中文总结
该研究基于BdG哈密顿量，在三个条件下揭示超导态量子几何可分解为正常态与配对量子几何的复合结构，推导了相关解析公式，为超导体设计及非常规超导电性实验诊断提供了依据。
AI 中文摘要
超导电性与正常态量子几何的相互作用近来已成为一系列研究的主题，尤其是关于超流体重量的研究。在本研究中，我们将注意力转向由Bogoliubov-de Gennes（BdG）哈密顿量所决定的超导态本身的量子几何，该哈密顿量支配着超导电性的几何与拓扑性质。我们证明，在三个一般性条件下，即超导适配性、超导配对的轨道均匀性以及无正常态自旋翻转项，BdG量子几何可精确分解为正常态量子几何与额外的配对量子几何之和，从而呈现出简单的复合结构。我们表明，这种分解适用于所有自旋单态和自旋三重态配对，包括非幺正自旋三重态配对。我们还为所有这些情况提供了配对量子几何的显式解析公式。这些结果确立了仅超导配对如何轻易驱动拓扑和有限量子度量，即使在无正常态量子几何的拓扑平庸或平带超导体中也存在这种情况。为补充这些结果，我们还推导了具有非均匀配对和有限超导适配性的一般两轨道自旋单态超导体的BdG量子几何。在此，我们的显式解析结果确立了不可分解的复合BdG量子几何，其中正常态和配对贡献通常相互交织，从而为有限量子几何提供了更多可能性。我们的结果为构建具有非平庸拓扑和有限量子度量的超导体及超导混合结构提供了设计规则，还将有助于非常规超导电性的实验诊断。
英文摘要
The interplay of superconductivity and the quantum geometry of the normal state has recently been the subject of an array of studies, especially regarding the superfluid weight. In this work, we turn our attention to the quantum geometry of the superconducting state itself, set by the Bogoliubov-de Gennes (BdG) Hamiltonian, which dictates the geometric and topological properties of superconductivity. We show that under three general conditions, namely superconducting fitness, orbital uniformity of the superconducting pairing, and absence of normal-state spin-flip terms, the BdG quantum geometry exactly separates into a sum of the normal-state quantum geometry and an additional pairing quantum geometry, thereby displaying a simple composite structure. We show that this separation holds for all spin-singlet and -triplet pairings, including nonunitary spin-triplet pairing. We further provide explicit analytical formulas for the pairing quantum geometry for all these cases. These results establish how superconducting pairing alone easily drives both topology and a finite quantum metric, thus being present even in topological trivial or flat band superconductors, with no normal state quantum geometry. To complement these results, we also derive the BdG quantum geometry of a general two-orbital spin-singlet superconductor with non-uniform pairing and finite superconducting fitness. Here, our explicit analytical results establish a non-separable composite BdG quantum geometry, with the normal state and pairing contributions generally intertwining, thereby producing even more possibilities for finite quantum geometry. Our results provide design rules for creating superconductors and superconducting hybrid structures with nontrivial topology and finite quantum metric and will additionally help in the experimental diagnosis of unconventional superconductivity.
