近日，复旦大学吴宜家团队报道了马约拉纳和狄拉克费米子零模非阿贝尔编织的统一模型。这一研究成果发表在2025年10月21日出版的《中国科学：物理学 力学 天文学》杂志上。

马约拉纳零模（MZMs）是研究最深入的非阿贝尔任意子。拓扑绝缘子中的狄拉克费米子零模是费米子数守恒下对称保护的MZM的加倍，为探索非阿贝尔任意子提供了另一种方法。然而，一个统一的用于阐明这些类型的拓扑零模式的编织统计的模型仍然缺乏。

研究组证明了超越微调区域的最小基塔耶夫链模型提供了MZM和狄拉克费米子零模在不同参数区域的非阿贝尔统计量的统一表征。特别地，他们引入了一个基于最小Kitaev链模型的最小三结设置，并证明了它有利于编织狄拉克费米子零模的统一方案，以及在狄拉克模辅助下的MZM。这个统一的最小模型提供了对非阿贝尔统计的更深入的见解，证明了MZM的非阿贝尔编织可以连续扩展到包含狄拉克费米子零模。

最小Kitaev链已经在耦合量子点中实现(Nature 614,445 (2023)；Nature 641, 890(2025))。该研究的推广证明了非阿贝尔MZM对和狄拉克零模的新非平凡相出现在更广泛的参数范围内，没有微调，扩大了可访问的实验参数空间，增强了在最小Kitaev链模型中观察非阿贝尔统计量的可行性。

附：英文原文

Title: Unified model for non-Abelian braiding of Majorana and Dirac fermion zero modes

Author: Huang, Tianyu, Zhang, Rui, Li, Xiaopeng, Liu, Xiong-Jun, Xie, X. C., Wu, Yijia

Issue&Volume: 2025-10-21

Abstract: Majorana zero modes (MZMs) are the most intensively studied non-Abelian anyons. The Dirac fermion zero modes in topological insulators, which are symmetry-protected doubling of MZMs under fermion number conservation, offer an alternative approach to explore non-Abelian anyons. However, a unified model that elucidates the braiding statistics of these types of topological zero modes remains absent. We show that the minimal Kitaev chain model beyond fine-tuning regime provides a unified characterization of the non-Abelian statistics of both MZMs and Dirac fermion zero modes in different parameter regimes. In particular, we introduce a minimal tri-junction setting based on the minimal Kitaev chain model and show it facilitates the unified scheme of braiding Dirac fermion zero modes, as well as the MZMs in the assistance of a Dirac mode. This unified minimal model provides deeper insights into non-Abelian statistics, demonstrating that the non-Abelian braiding of MZMs can be continuously extended to encompass Dirac fermion zero modes. The minimal Kitaev chain has been realized in coupled quantum dots (Nature 614, 445 (2023); Nature 641, 890 (2025)). Our extension, which demonstrates novel nontrivial phases with non-Abelian MZM pairs and Dirac zero modes emerging in the broader parameter regimes without fine-tuning, expands the accessible experimental parameter space and enhances the feasibility of observing non-Abelian statistics in the minimal Kitaev chain model.

DOI: 10.1007/s11433-025-2808-x

Source: https://link.springer.com/article/10.1007/s11433-025-2808-x