[论文解读] Imaging inter-valley coherent order in magic-angle twisted trilayer graphene

Hyunjin Kim, Youngjoon Choi+13 more|arXiv (Cornell University)|Apr 20, 2023

Quantum and electron transport phenomena被引用 8

一句话总结

本论文使用扫描隧道显微镜观察魔角扭曲三层石墨烯中的电子对称性破缺，揭示掺杂相关的跨谷（inter-valley）相干 Kekulé 阶序及其非整比螺旋调制。

ABSTRACT

Magic-angle twisted trilayer graphene (MATTG) exhibits a range of strongly correlated electronic phases that spontaneously break its underlying symmetries. The microscopic nature of these phases and their residual symmetries stands as a key outstanding puzzle whose resolution promises to shed light on the origin of superconductivity in twisted materials. Here we investigate correlated phases of MATTG using scanning tunneling microscopy and identify striking signatures of interaction-driven spatial symmetry breaking. In low-strain samples, over a filling range of about 2-3 electrons or holes per moiré unit cell, we observe atomic-scale reconstruction of the graphene lattice that accompanies a correlated gap in the tunneling spectrum. This short-scale restructuring appears as a Kekulé supercell -- implying spontaneous inter-valley coherence between electrons -- and persists in a wide range of magnetic fields and temperatures that coincide with the development of the gap. Large-scale maps covering several moiré unit cells further reveal a slow evolution of the Kekulé pattern, indicating that atomic-scale reconstruction coexists with translation symmetry breaking at the much longer moiré scale. We employ auto-correlation and Fourier analyses to extract the intrinsic periodicity of these phases and find that they are consistent with the theoretically proposed incommensurate Kekulé spiral order. Moreover, we find that the wavelength characterizing moiré-scale modulations monotonically decreases with hole doping away from half-filling of the bands and depends only weakly on the magnetic field. Our results provide essential insights into the nature of MATTG correlated phases in the presence of strain and imply that superconductivity emerges from an inter-valley coherent parent state.

研究动机与目标

• 识别魔角扭曲三层石墨烯（MATTG）中对称性破缺电子相的实空间特征。
• 表征跨谷相干（IVC）序在 STM 数据中的表现及其与电子能隙的关系。
• 确定 Kekulé 类序在 MATTG 中的波矢、掺杂依赖性和应变敏感性。
• 通过空间布置与场/温度依赖性区分可能的 IVC 情况（T-IVC vs IKS）。

提出的方法

• 在近魔角（1.60°）的低应变 MATTG 上进行高分辨率的 STM/dI/dV 映射，利用受控栅控改变填充因子 ν。
• 使用傅里叶分析识别 Kekulé 型晶格增大并从 FT 谱的卫星峰中提取 q_Kekulé。
• 应用 Kekulé 自相关与区域逐区 FT 过滤，研究莫尔条纹尺度区域内畸变的空间演化。
• 将观测到的波矢与模式与理论的 IKS（非整比 Kekulé 螺旋）及 T-IVC 情景相比对，同时考虑异源应变。
• 研究栅极电压、偏压、温度和磁场对电子起源的重构的依赖性，以确认其电子起源。

Fig. 1: Overview of the experiment and atomically resolved maps revealing Kekulé pattern. a , Schematic depicting twisted trilayer graphene (up) and device geometry used for the STM measurements (down). b , Atomically resolved topography showing the moiré lattice used to extract hetero-strain magnit

实验结果

研究问题

• RQ1 MATTG 是否在 STM 的 LDOS 映射中表现出通过 Kekulé 类晶格三重化来体现的跨谷相干序？
• RQ2 Kekulé 模式的波矢 q_Kekulé 及其对填充、应变和磁场的依赖性，以及与 IKS 预测的对比？
• RQ3 STM 测量能否基于零场特征与场依赖区分 MATTG 的 IVC 相（IKS vs T-IVC）？
• RQ4 异源应变如何影响观测到的 IVC 相关模式及其与莫尔晶格的整数性？

主要发现

• 在充填约 -3<ν<-2 与 2<ν<3 时，dI/dV 映射中出现 Kekulé 型晶格三重化模式，指示跨谷相干。
• Kekulé 模式在电荷中性点及远端能带附近缺失，其强度随相关能隙变化，在多场与多温度范围内持久存在。
• 傅里叶分析揭示 Kekulé 调制波矢 q_Kekulé 通常与莫尔势场不整比，并随空穴掺杂而减小/增大，在穿过莫尔布里努旺区界附近到达准共整点。
• 自相关与 FT 过滤分析显示莫尔尺度的平移对称性破坏以及 Kekulé 模式在多个莫尔单元胞内的缓慢演化，与 IKS 型序一致。
• 提取的 q_Kekulé 与含异源应变的 IKS 理论吻合，并与空穴掺杂的实验趋势一致，支持以跨谷巢穴驱动的螺旋序作为 MATTG 超导的母态。
• 其他观测包括 FT 图中的条纹状斜带特征，表明在电荷中性附近存在 C3 对称性破缺和石墨烯键向的方向性，提示 nematic 倾向。

Fig. 2: $\mathbf{V_{\rm Gate}}$ dependent mapping of Kekulé order on MATTG. a-d , Real space $dI/dV$ map at $V_{\rm Gate}=-20$ V ( a ), $-10$ V ( b ), $0$ V ( c ), $9$ V ( d ), taken at $V_{\rm Bias}=63$ mV ( a ), $-3$ mV ( b ), $-13$ mV ( c ), $3$ mV ( d ), tracking the evolution of the flat band d