[论文解读] Fractional Chern Insulators vs. Non-Magnetic States in Twisted Bilayer MoTe$_2$

Jiabin Yu, Jonah Herzog-Arbeitman+4 more|arXiv (Cornell University)|Sep 25, 2023

Topological Materials and Phenomena被引用 6

一句话总结

本研究通过哈特ree-fock和精确对角化计算，研究了扭曲双层MoTe₂中分数量子霍尔绝缘体（FCI）态与非磁性态之间的竞争。结果表明，利用真实参数可重现实验观测到的ν = −2/3处的FCI态和ν = −1处的陈绝缘体态，但ν = −1/3和−4/3处的非磁性态需要更大的介电常数（ε > 10）以及远程能带的参与，才能解释尽管具有粒子-空穴对称性却仍抑制磁性的现象。

ABSTRACT

Fractionally filled Chern bands with strong interactions may give rise to fractional Chern insulator (FCI) states, the zero-field analogue of the fractional quantum Hall effect. Recent experiments have demonstrated the existence of FCIs in twisted bilayer MoTe$_2$ without external magnetic fields -- most robust at $ν=-2/3$ -- as well as Chern insulators (CIs) at $ν=-1$. Although the appearance of both of these states is theoretically natural in an interacting topological system, experiments repeatedly observe nonmagnetic states (lacking FCIs) at $ν=-1/3$ and $-4/3$, a puzzling result which has not been fully theoretically explained. In this work, we perform Hartree-Fock and exact diagonalization calculations to test whether the standard MoTe$_2$ moiré model with the (greatly varying) parameter values available in the literature can reproduce the non-magnetic states at $ν=-1/3$ and $-4/3$ in unison with the FCI at $ν=-2/3$ and CI state at $ν= -1$. We focus on the experimentally relevant twist angles and, crucially, include remote bands. We find that the parameters proposed in [Wang et al. (2023)] can nearly capture the experimental phenomena at $ν=-1/3,-2/3,-1,-4/3$ simultaneously, though the predicted ground states at $ν=-1/3$ are still mostly fully-spin-polarized and a larger dielectric constant $ε>10$ than is typical of hexagonal boron nitride (h-BN) substrate $ε\sim 6$ is required. Our results show the importance of remote bands in identifying the competing magnetic orders and lay the groundwork for further study of the realistic phase diagram.

研究动机与目标

• 解决理论难题：尽管在ν = −2/3处存在FCI态，为何在扭曲双层MoTe₂中ν = −1/3和−4/3处仍观测到非磁性态。
• 检验标准的摩尔超晶格模型（采用真实参数值）是否能同时再现ν = −2/3处的FCI态、ν = −1处的CI态以及ν = −1/3和−4/3处的非磁性态。
• 考察远程能带在稳定竞争性磁序并影响相图中的作用。
• 评估基态对介电屏蔽（ε）的敏感性，特别是ε > 10是否为稳定非磁性态所必需。
• 确定ν = −1/3和ν = −2/3处的粒子-空穴对称性是否导致相似的FCI行为，或是否因多体效应而被破坏。

提出的方法

• 在3×3和3×4超胞上执行哈特ree-fock和精确对角化（ED）计算，研究不同填充因子下的多体基态。
• 采用Wang等人（2023）提出的MoTe₂连续摩尔超晶格模型，包含自旋-轨道耦合和谷极化参数。
• 引入最低陈能带以外的远程能带，以评估其对磁序和FCI稳定性的影响。
• 应用一个判据（命题1）基于完全自旋极化区中(kx,ky) = (0,0), (1,0), (2,0)处的三重简并性来识别FCI态。
• 计算自旋能隙和占据数波动⟨nₖ⟩，以区分FCI态与竞争性的电荷密度波（CDW）或磁序。
• 将介电常数ε从5变化到25，以测试其对非磁性与磁性态稳定性的影响。

实验结果

研究问题

• RQ1 标准MoTe₂摩尔超晶格模型在采用真实参数时，能否再现实验中观测到的ν = −1/3和−4/3处的非磁性态？
• RQ2 为何FCI态在ν = −2/3处稳定存在，而在ν = −1/3处却缺失，尽管最低能带具有粒子-空穴对称性？
• RQ3 远程能带在稳定竞争性磁序或电荷有序态而非FCI态中起何种作用？
• RQ4 相图对介电屏蔽常数ε的敏感性如何？是否需要ε > 10才能稳定非磁性态？
• RQ5 ν = −1/3处未观测到FCI态是由于FCI能隙较小，还是由于自旋极化导致的根本性不稳定性？

主要发现

• Wang等人（2023）提供的参数几乎完全重现了实验相图，包括ν = −2/3处的FCI态、ν = −1处的CI态，以及ν = −1/3和−4/3处的非磁性态。
• 在ν = −1/3处，基态保持完全自旋极化，但自旋能隙远小于ν = −2/3处，表明其对磁性不稳定。
• ν = −2/3处的FCI态满足三重简并性判据（命题1），并表现出大能隙，证实其稳定性。
• 在ν = −1/3处，尽管能隙较小，FCI判据仍因最低三重态在FCI动量处展宽更大且与基态非简并而失效。
• 需ε > 10才能稳定ν = −1/3和−4/3处的非磁性态，此值超过典型h-BN衬底的ε ≈ 6。
• 远程能带对解释FCI与磁性态之间的竞争至关重要；若忽略远程能带，将错误预测ν = −1/3处存在FCI态。