AI 中文总结
本研究针对二维平带超导体中磁性吸附原子诱导的YSR束缚态，揭示了其空间分布的二次展宽依赖杂质可调、局域化长度具有普适性的特性，实现了两类物理的清晰分离并通过数值验证。
AI 中文摘要
在平带超导体中，主导配对与输运的是量子几何而非动能。然而，这种几何特性在对局域、可单独寻址的杂质的响应中如何体现，目前仍很大程度上未被探索。本文中，我们研究了由磁性吸附原子诱导的Yu-Shiba-Rusinov（YSR，宇志波-柴田-鲁西诺夫）束缚态——该吸附原子与二维平带超导体的每个轨道发生杂化，并通过两个物理量表征其空间分布：二次展宽$Q_S$和局域化长度$ξ$。我们发现，$Q_S$并非仅由量子度规决定：轨道间干涉产生的几何修正，以及更重要的、吸附原子-晶格杂化的各向异性带来的修正，均以同等权重起作用，使得$Q_S$强烈依赖于杂质且可调。另一方面，$ξ$仅由平带上的投影产生，是由紧致局域态交叠决定的普适特性。所有杂质依赖性反而被隔离在波函数的 prefactor（ prefactor，前因子）中，其大小与$Q_S$直接相关。因此，我们报道了这些系统中诱导YSR束缚态的普适物理与杂质可调物理之间的清晰分离，并通过精确对角化的数值计算验证了我们的结果。
英文摘要
In flat band superconductors, quantum geometry, rather than kinetic energy, governs pairing and transport. However, how this geometry manifests in the response to a local, individually addressable impurity remains largely unexplored. Here, we study the Yu-Shiba-Rusinov (YSR) bound state induced by a magnetic adatom that hybridizes with every orbital of a two-dimensional flat band superconductor, and characterize its spatial profile using two quantities: the quadratic spread $Q_S$ and the localization length $ξ$. We show that $Q_S$ is not set by the quantum metric alone, as geometric corrections arising from inter-orbital interference and, more importantly, from the anisotropy of the adatom-lattice hybridization contribute on equal footing, making $Q_S$ strongly impurity dependent and tunable. On the other hand, $ξ$ emerges from the projection onto the flat band alone and is a universal property set by the overlap of compact localized states. All impurity dependence is instead isolated in the prefactor of the wavefunction whose magnitude correlates directly with $Q_S$. We, therefore, report a clean separation between universal and impurity-tunable physics from the induced YSR bound state in these systems, and confirm our results numerically via exact diagonalization.
Comments7 pages, 5 figures
