$1/3$-通量束缚态在多组分超导体中展现$\mathbb {Z}_3$ parafermions的非阿贝尔统计

中文摘要 AI 辅助

多组分超导体（MSCs）被预测可承载携带超导通量量子任意分数的磁通量子。近期进展提高了在具有$C_3$旋转对称性的多组分超导体中出现$1/3$通量量子的期望。长期以来，束缚于这种分数通量的电子被认为形成任意子，然而其明确的编织统计尚未被探索。我们提出这些1/3通量束缚态（1/3-FBSs）展现出$\mathbb{Z}_3$ parafermions的有趣非阿贝尔统计。在无双重占据约束下，1/3-FBSs的两次连续编织操作等价于单次$\mathbb Z_3$ parafermion编织操作。编码编织结果的parafermion奇偶性可通过1/3-FBSs的费米子占据数读出。结合交叉安德烈反射诱导的Hadamard门，可以实现完整的$\mathbb{Z}_3$ parafermion编织操作集合。

英文摘要

Multicomponent superconductors (MSCs) are predicted to host magnetic flux quanta carrying arbitrary fractions of the superconducting flux quantum. Recent advances have raised the expectation that $1/3$ flux quanta may emerge in MSCs with $C_3$ rotational symmetry. Electrons bound to such fractional flux are long regarded to form anyons, yet their explicit braiding statistics remain unexplored. We propose that these $1/3$-flux bound states ($1/3$-FBSs) exhibit the intriguing non-Abelian statistics of $\mathbb{Z}_3$ parafermions. Under no-double-occupancy constraint, two successive braiding operations of $1/3$-FBSs are equivalent to a single $\mathbb Z_3$ parafermion braiding operation. The parafermion parity encoding the braiding outcome can be read out via the fermionic occupation number of the $1/3$-FBSs. Combined with a crossed-Andreev-reflection-induced Hadamard gate, one can realize the complete set of $\mathbb{Z}_3$ parafermion braiding operations.

发表机构

• Interdisciplinary Center for Theoretical Physics and Information Sciences, Fudan University（复旦大学理论物理与信息科学交叉中心）
• State Key Laboratory of Surface Physics and Department of Physics, Fudan University（复旦大学表面物理国家重点实验室和物理系）
• Shanghai Research Center for Quantum Sciences（上海量子科学研究中心）
• International Center for Quantum Materials, School of Physics, Peking University（北京大学物理学院量子材料国际中心）
• Hefei National Laboratory（合肥国家实验室）

机构由 AI 辅助整理，请以论文原文为准。

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6 pages, 1 figure