[论文解读] Anomalous Hall Crystals in Rhombohedral Multilayer Graphene I: Interaction-Driven Chern Bands and Fractional Quantum Hall States at Zero Magnetic Field

Junkai Dong, Taige Wang+5 more|arXiv (Cornell University)|Nov 9, 2023

Graphene research and applications参考文献 82被引用 6

一句话总结

该论文提出，在三角形堆叠的五层石墨烯中，由电子相互作用驱动的拓扑序可导致在零磁场下出现一个鲁棒且孤立的陈数为 |C|=1 的陈能带，从而实现分数量子反常霍尔态。通过自洽哈特ree-Fock和精确对角化方法，作者识别出一种自发时间平移对称性破缺的态——称为‘反常霍尔晶体’——即使在无莫尔势的情况下也能稳定拓扑序。

ABSTRACT

Recent experiments on rhombohedral pentalayer graphene flakes with a substrate induced moiré potential have identified both Chern insulators and fractional Quantum Hall states in the absence of an applied magnetic field. Surprisingly, these states are observed in strong displacement fields where the effects of the moiré lattice are weak, and seem to be readily accessed without fine-tuning. To address these experimental puzzles we study an interacting model of electrons in this geometry, first within the self-consistent Hartree-Fock (SCHF) approximation. We find an isolated Chern band with Chern number $|C|=1$, that moreover is relatively flat and shows good quantum geometry. Exact diagonalization and density matrix renormalization group methods at fractional filling establish the presence of fractional quantum anomalous Hall (FQAH) states. The $|C|=1$ band in SCHF is remarkably robust to varying microscopic parameters, and is also found in the $N_L=4$ and $N_L=6$ layer systems. Remarkably, it appears stable even to switching off the moiré potential, pointing to spontaneous breaking of translation symmetry. We term this topological crystalline state the ``anomalous Hall crystal" (AHC), and argue that it constitutes a general mechanism for creating stable Chern bands in rhombohedral graphene. Our work elucidates the physics behind the recent rhombohedral pentalayer graphene observations, predicts the appearance of the same phase in other systems, and opens the door to studying the interplay between electronic topology and spontaneous translation symmetry breaking.

研究动机与目标

• 解决在无外加磁场条件下，实验观测到的三角形堆叠五层石墨烯中陈绝缘体和分数量子霍尔态的成因。
• 确定在强位移场下实验观测到的鲁棒 |C|=1 陈能带的起源。
• 探究该拓扑态是否源于电子关联而非单体能带结构。
• 研究在无莫尔势条件下，不同层数（NL = 4, 5, 6）下陈能带的稳定性。
• 识别一种新的拓扑晶体相——‘反常霍尔晶体’，其通过自发时间平移对称性破缺稳定拓扑序。

提出的方法

• 采用自洽哈特ree-Fock（SCHF）计算求解三角形堆叠多层石墨烯中存在与不存在莫尔势时的相互作用多体问题。
• 在圆柱几何下使用精确对角化（ED）和密度矩阵重整化组（DMRG）探测在分数填充率下的分数量子反常霍尔（FQAH）态。
• 通过从最低哈特ree-Fock能带导出的形式因子，将系统映射到单带有效哈密顿量，从而实现对拓扑关联的模拟。
• 在DMRG模拟中应用MPO压缩技术，以低于10⁻² meV的误差高效表示长程库仑相互作用。
• 通过纠缠谱分析诊断拓扑序，确认其简并度计数与分拆数 1,1,2,3,5,7,… 一致。
• 通过子采样实现磁通插入，展示准简并基态之间的能谱流，从而证实拓扑序的存在。

Figure 1: (a) Geometry of rhombohedral pentalayer graphene on hBN. The bottom layer of rhombohedral pentalayer graphene sits on top of hBN with a relative twist $\theta$ . Positive potential differences $u_{D}>0$ between layers polarizes conduction electrons away from the hBN layer. (b) The energy d

实验结果

研究问题

• RQ1 在零磁场下，三角形堆叠五层石墨烯中观测到的鲁棒 |C|=1 陈能带的微观起源是什么？
• RQ2 电子相互作用驱动的拓扑序是否能在无外加磁场条件下稳定分数量子反常霍尔态？
• RQ3 当莫尔势被关闭时，陈能带是否仍保持稳定？其稳定机制是什么？
• RQ4 在 NL = 4 和 NL = 6 的多层体系中，是否会出现相同的拓扑相？
• RQ5 稳定陈能带的自发对称性破缺态的本质是什么？

主要发现

• 在自洽哈特ree-Fock解中，即使在无莫尔势条件下，仍可出现一个稳定且具有高量子几何和能带平坦度的 |C|=1 陈能带。
• 在无莫尔势条件下，当位移场 uD > 25 meV 时，反常霍尔晶体（AHC）相——其特征为时间平移对称性的自发破缺——成为基态。
• 通过精确对角化和DMRG确认了分数量子反常霍尔态的存在，其纠缠谱表现出特征简并度计数 1,1,2,3,5,7,…
• |C|=1 陈能带在不同莫尔势、跃迁参数和层数（NL = 4, 5, 6）下均保持鲁棒，表明其具有普适机制。
• AHC相的相变发生在临界位移场 uD*，该值随层数 NL 增加而减小。
• 即使在关闭莫尔势的情况下，AHC相依然稳定，表明电子-电子相互作用本身即可通过自发对称性破缺稳定拓扑序。

Figure 2: (a) The phase diagram of moiré rhombohedral pentalayer graphene as a function of the interlayer potential difference $u_{D}$ , and the twist angle $\theta$ . The colors label the Chern number of the SCHF ground states, with gapless regions shown in white. On the moiré distant side ( $u_{D}