发表机构
Yonsei University; The University of Tokyo; RIKEN Nishina Center（延世大学; 东京大学; 理化学研究所仁科加速器研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过谱交叉标度律区分融合与分裂的量子化涡旋，提出利用失谐标度指数及交叉行为实现低于成像分辨率的涡旋结构光谱诊断。
AI 中文摘要
一个电荷为$r$的耦合涡旋在弱对称性破缺后，可以保持为一个融合的$r$阶零点，或分裂为$r$个邻近的单位电荷零点。这两种构型具有相同的总绕数和最低朗道能级投影中相同的暗态数目，因此施加的轨道角动量和总绕数都无法区分它们的局域几何。我们在由拉曼场耦合的双组分Haldane球模型中研究这一区分。对于磁单极通量$N$，缺陷分支穿越零能量的失谐$\tau_{\rm c}$在融合零点情形下按$|\tau_{\rm c}|\sim N^{-(r+1)}$标度，在分辨单位零点情形下按$N^{-2}$标度。Feshbach约化建立了完整多带哈密顿量的这些渐近定律，而基于单极谐波基的数值计算确认了$r=1,2,3$的融合涡旋标度。对于直径为$d$的部分分裂团簇，当$d$与磁长度$\tellell_B$相当时，标度发生交叉，从而即使在直接成像的空间分辨率以下，也可以通过光谱方法推断出$d$。
英文摘要
A charge-$r$ coupling vortex can remain as one fused order-$r$ zero or split into $r$ nearby unit-charge zeros after weak symmetry breaking. The two configurations have the same total winding and the same number of dark states in the lowest-Landau-level projection, so neither the imposed orbital angular momentum nor the total winding number distinguishes their local geometry. We study this distinction in a two-component Haldane-sphere model coupled by a Raman field. For monopole flux $N$, the detuning $τ_{\rm c}$ at which a defect branch crosses zero energy scales as $|τ_{\rm c}|\sim N^{-(r+1)}$ for a fused zero and $N^{-2}$ for resolved unit zeros. A Feshbach reduction establishes these asymptotic laws for the full multiband Hamiltonian, and numerical calculations in a monopole-harmonic basis confirm the fused-vortex scaling for $r=1,2,3$. For a partially split cluster of diameter $d$, the scaling crosses over when $d$ is comparable to the magnetic length $\ell_B$, allowing $d$ to be inferred spectroscopically even below the spatial resolution of direct imaging.
Comments5 pages, 3 figures; Supplemental Material included
