发表机构
University of California, Berkeley; Harvard University; University of Maryland, College Park; University of Pittsburgh（加州大学伯克利分校; 哈佛大学; 马里兰大学帕克分校; 匹兹堡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文构建了(2+1)维有隙超导体的分类框架，发现了SC$^\boldsymbol{\u266f}$家族这一新的超导相，其基本涡旋无法分解且必为非阿贝尔，还开发代数框架构建示例并约束拓扑有序超导体的实现。
AI 中文摘要
超导电性与内禀拓扑序可以超越简单共存的方式交织。本文针对具有凝聚电荷$2ne$的(2+1)维有隙超导体，构建了一套分类框架，通过聚焦超导涡旋的拓扑性质，精准刻画这种交织作用，得到了交织程度递增的分类结果：从无拓扑序的熟知可逆超导体，到未扭曲与扭曲的SC$^\boldsymbol{\u2217}$，最终到SC$^\boldsymbol{\u266f}$。核心发现是SC$^\boldsymbol{\u266f}$家族，其中携带$h/(2ne)$通量的基本涡旋无法分解为被任意子修饰的可逆超导体涡旋，且每个基本涡旋必然是非阿贝尔的。对于这类相，还得到了禁区结果：基本涡旋扇区的量子维度至少为$\boldsymbol{\u221a6}$，且无法满足斐波那契融合规则。本文开发了一套系统的代数框架，通过任意子凝聚得到所有这些超导相，由此构建了多个无限族示例，并与任意子超导电性建立联系。最后，引入了原始SC$^\boldsymbol{\u266f}$相，其所有非平凡涡旋扇区的分解均受阻，且论证了它们无法通过低电荷超导凝聚体相对相位的无序化产生。这套基于涡旋性质的分类方案，揭示了拓扑有序超导体间的新区分，并约束了它们的实现方式。
英文摘要
Superconductivity and intrinsic topological order can intertwine in ways that go beyond simple coexistence. Here we develop a classification framework for (2+1)D gapped superconductors with condensate charge $2ne$. By focusing on the topological properties of superconducting vortices, we precisely characterize this interplay. We obtain a classification with increasing levels of intertwinement, from the well known invertible superconductors without topological order, to untwisted and twisted SC$^\ast$, and finally to SC$^{\sharp}$. Our main finding is the family SC$^{\sharp}$, in which the elementary vortex carrying $h/(2ne)$ flux cannot be factorized into an invertible superconductor vortex dressed by bulk anyons, and every elementary vortex is necessarily non-Abelian. For such phases, we also obtain no-go results: the elementary vortex sector has quantum dimension at least $\sqrt{6}$ and cannot satisfy Fibonacci fusion rules. We develop a systematic algebraic framework to obtain all these superconducting phases through anyon condensation, allowing us to construct several infinite families of examples and make connections to anyon superconductivity. Finally, we introduce primitive SC$^\sharp$ phases for which factorization of every nontrivial vortex sector is obstructed, and argue that they cannot arise by disordering the relative phases of lower-charge superconducting condensates. Our classification scheme based on vortex properties allows us to uncover new distinctions between topologically ordered superconductors and constrain how they can be realized.
Comments15+10 pages, 1+0 figures
