AI 中文总结
本文在扭转双层棋盘晶格模型中，通过量子几何嵌套诱导出精确配对密度波（PDW）基态，并推导得到非简并量子几何嵌套超导体超流刚度的普适关系，揭示了PDW序、量子几何与能带拓扑的相互作用。
AI 中文摘要
配对密度波（PDW）是超越BCS范式的非常规超导态，但由于存在多种竞争序，在微观晶格模型中明确识别它们通常颇具挑战。特别是，在具有拓扑能带的相互作用模型中实现精确PDW的目标仍难以达成。本文中，我们在具有拓扑平带的扭转双层棋盘晶格（TBCB）上构建了一个相互作用模型，并基于其动量空间非对称对称，严格证明了量子几何嵌套（QGN）可诱导出精确的PDW基态。我们进一步证明，任何非简并QGN超导体（包括本文研究的PDW和均匀超导体）的超流刚度满足普适关系$D_s=2N_{\rm flat}\nu(1-\nu)m_{\rm pair}^{-1}$，其中$N_{\rm flat}$为平带数目，$\nu$为平带填充率，$m_{\rm pair}$为两粒子有效质量。本研究揭示了PDW序、量子几何与能带拓扑之间存在丰富的相互作用。
英文摘要
Pair-density waves (PDWs) are unconventional superconducting states beyond the BCS paradigm, but identifying them unambiguously in microscopic lattice models is generally challenging due to various competing orders. In particular, an exact realization of PDW in interacting models with topological bands remains elusive. Here we construct an interacting model on a twisted bilayer checkerboard lattice (TBCB) featuring topological flat bands, and rigorously show that an exact PDW ground state can be induced by quantum geometric nesting (QGN), owing to its momentum-space nonsymmorphic symmetry. We further prove that the superfluid stiffness of any nondegenerate QGN superconductor (including the PDW studied here and uniform superconductor) obeys the universal relation $D_s=2N_{\rm flat}ν(1-ν)m_{\rm pair}^{-1}$, where $N_{\rm flat}$, $ν$, and $m_{\rm pair}$ are the number of flat bands, flat band filling, and the two-particle effective mass, respectively. Our results reveal a rich interplay among PDW order, quantum geometry, and band topology.
Comments4 pages, 2 figures
