调制Bernal石墨烯中的Read-Rezayi分数量子霍尔绝缘体

中文摘要 AI 辅助

Fibonacci任意子为拓扑量子计算提供了通用平台，并作为分数量子霍尔效应中$\mathbb{Z}_3$ Read-Rezayi相的低能激发出现。然而，在无磁场条件下该相的现实微观实现仍然难以捉摸。我们研究了一个具有栅极屏蔽库仑相互作用的周期性调制Bernal双层石墨烯模型。利用最近发展的目标相位优化方法结合能带投影精确对角化，我们在填充因子$\nu=3/5$处识别出一个参数空间区域，其基态与Read-Rezayi分数量子霍尔绝缘体一致。产生该态的未完全填充能带是一个双能带复合体的一部分，该复合体模仿了最低和第一朗道能级的几何方面，且$\nu=1/2$处的基态与Moore-Read态一致。我们的结果表明，调制Bernal石墨烯可以在零磁场下实现精细的非阿贝尔分数量子霍尔态，同时展示了目标相位优化作为在现实高维微观模型中发现此类相的实际途径。

英文摘要

Fibonacci anyons provide a universal platform for topological quantum computation, and emerge as low-energy excitations in the $\mathbb{Z}_3$ Read-Rezayi phase in the fractional quantum Hall effect. However, realistic microscopic realizations of this phase in the absence of a magnetic field have remained elusive. We study a model of periodically modulated Bernal bilayer graphene with gate-screened Coulomb interactions. Using the recently developed target-phase optimization method in conjunction with band-projected exact diagonalization, we identify at filling $ν=3/5$ a region of parameter space whose ground state is consistent with a Read-Rezayi fractional Chern insulator. The partially filled band from which it arises is a part of a two-band complex which mimics geometric aspects of the lowest and first Landau levels, with the ground state at $ν=1/2$ consistent with the Moore-Read state. Our results suggest that modulated Bernal graphene can realize delicate non-Abelian fractional quantum Hall states at zero magnetic field, while demonstrating target-phase optimization as a practical route to discovering such phases in realistic, high-dimensional microscopic models.

发表机构

• Massachusetts Institute of Technology（麻省理工学院）
• Universitat Politècnica de Catalunya（加泰罗尼亚理工大学）
• Stockholm University（斯德哥尔摩大学）
• KTH Royal Institute of Technology（瑞典皇家理工学院）
• Uppsala University（乌普萨拉大学）

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