[论文解读] Local probe of bulk and edge states in a fractional Chern insulator

Zhurun Ji, Heonjoon Park+7 more|arXiv (Cornell University)|Apr 10, 2024

Topological Materials and Phenomena被引用 5

一句话总结

作者使用激子共振微波阻抗显微镜（ER-MIM）对扭曲的 MoTe2 中的零磁场分数量子霍尔绝缘体的 bulk 与 edge 状态进行成像，揭示体相绝缘但边界导电，以及在拓扑转变中的边缘演化。

ABSTRACT

Fractional quantum Hall effect (FQHE) is a prime example of topological quantum many-body phenomena, arising from the interplay between strong electron correlation, topological order, and time reversal symmetry breaking. Recently, a lattice analog of FQHE at zero magnetic field has been observed, confirming the existence of a zero-field fractional Chern insulator (FCI). Despite this, the bulk-edge correspondence -- a hallmark of FCI featuring an insulating bulk with conductive edges -- has not been directly observed. In fact, this correspondence has not been visualized in any system for fractional states due to experimental challenges. Here we report the imaging of FCI edge states in twisted MoTe2 by employing a newly developed modality of microwave-impedance microscopy. By tuning the carrier density, we observe the system evolving between metallic and FCI states, the latter of which exhibits insulating bulk and conductive edges as expected from bulk-boundary correspondence. We also observe the evolution of edge states across the topological phase transition from an incompressible Chern insulator state to a metal and finally to a putative charge ordered insulating state as a function of interlayer electric field. The local measurement further reveals tantalizing prospects of neighboring domains with different fractional orders. These findings pave the way for research into topologically protected 1D interfaces between various anyonic states at zero magnetic field, such as topological entanglement entropy, Halperin-Laughlin interfaces, and the creation of non-abelian anyons.

研究动机与目标

• 在零磁场分数量子霍尔绝缘体（FCI）中，使用局部探针展示bulk-edge对应关系。
• 可视化FCI态中的边缘态并将其与平凡绝缘态区分开。
• 探索由垂直电场驱动的拓扑相变中边缘态的演化。
• 在零磁场下，研究空间非均匀性以及不同分数量之间的域边界。

提出的方法

• 开发激子共振微波阻抗显微术（ER-MIM），通过顶栅实现双门控成像，以 WS2 作为光学门。
• 使用 MIM-Im（微波信号的虚部）作为局部电导率和在 GHz 频率下的电子压缩性的代理。
• 调整载流子密度和层间电场，以在扭曲 MoTe2 双层中进入 QAH 与 FCI 区域。
• 将 MIM-Im 映射为填充因子 ν 的函数，以识别 bulk 绝缘与 edge 导电行为。
• 进行有限元仿真以将 MIM-Im 与二维片状电导率相关，并验证空间分辨率。

Figure 1 : Local probe of bulk fractional Chern insulator (FCI) states. a . Schematic of the exciton-resonant microwave impedance microscopy setup, and the t-MoTe 2 device. The dual gated device has a monolayer WS 2 top gate (V ${}_{\text{tg}}$ ) and a graphite bottom gate (V ${}_{\text{bg}}$ ). b .

实验结果

研究问题

• RQ1 在莫尔尺度的系统中，是否可以在零磁场直接可视化 FCI 边缘态？
• RQ2 FCI 状态是否在局部测量中表现出与体边界对应一致的体绝缘与边缘导电？
• RQ3 在由层间电场驱动的拓扑相变中，分数量边缘态如何演化？
• RQ4 莫尔错配（moiré）无序和域形成在分数量边缘态的表现中起到怎样的作用？

主要发现

• ER-MIM 成像在 ν = -2/3 与 -3/5 FCI 状态下显示体绝缘、边缘导电，符合 bulk-edge 对应关系。
• 边缘态宽度在 QAH 与 FCI 区间约为 500 nm，宽于探针分辨率，可能是由于边缘磁等离子体模的缘故。
• FCI 状态边缘的 MIM-Im 信号高于 QAH 边缘，表明边缘动力学或磁等离子共振频率不同。
• 在相邻区域观察到不同分数量级的共存（例如 -3/5 与 -2/3），由门控变化引起，意味着可调的任意子顺序之间的一维界面。
• 电场驱动的转变显示边缘信号在中间的 D/ε0 时最强，表明在 Chern 到绝缘体转变过程中带隙关闭和一个金属性相中的中间相。
• 直接可视化确认分数量边缘态并非简单的边缘充电，而是源自零磁场下的体-边界物理。

Figure 2 : Imaging quantum anomalous Hall edge states. a , First panel: an AFM image of the sample, showing the edges and interfaces (gray and green dashed lines, respectively) and the scanning region (black rectangle). Scale bar: 1 $\mu$ m. Other panels: Real-space maps of the imaginary microwave r