[论文解读] Magic Angle Spectroscopy

Alexander Kerelsky, L. J. McGilly+10 more|MPG.PuRe (Max Planck Society)|Dec 20, 2018

Graphene research and applications被引用 228

一句话总结

本论文使用 STM/STS 映射原子尺度结构与近魔角扭曲双层石墨烯中的局部态密度，揭示了两个 van Hove singularities 的分离及其随角度和掺杂演化的相关性诱导的能-gap，并有 nematic order 的证据。

ABSTRACT

The electronic properties of heterostructures of atomically-thin van der Waals (vdW) crystals can be modified substantially by Moiré superlattice potentials arising from an interlayer twist between crystals. Moiré-tuning of the band structure has led to the recent discovery of superconductivity and correlated insulating phases in twisted bilayer graphene (TBLG) near the so-called "magic angle" of $\sim$1.1°, with a phase diagram reminiscent of high T$_c$ superconductors. However, lack of detailed understanding of the electronic spectrum and the atomic-scale influence of the Moiré pattern has so far precluded a coherent theoretical understanding of the correlated states. Here, we directly map the atomic-scale structural and electronic properties of TBLG near the magic angle using scanning tunneling microscopy and spectroscopy (STM/STS). We observe two distinct van Hove singularities (vHs) in the LDOS which decrease in separation monotonically through 1.1° with the bandwidth (t) of each vHs minimized near the magic angle. When doped near half Moiré band filling, the conduction vHs shifts to the Fermi level and an additional correlation-induced gap splits the vHs with a maximum size of 7.5 meV. We also find that three-fold (C$_3$) rotational symmetry of the LDOS is broken in doped TBLG with a maximum symmetry breaking observed for states near the Fermi level, suggestive of nematic electronic interactions. The main features of our doping and angle dependent spectroscopy are captured by a tight-binding model with on-site (U) and nearest neighbor Coulomb interactions. We find that the ratio U/t is of order unity, indicating that electron correlations are significant in magic angle TBLG. Rather than a simple maximization of the DOS, superconductivity arises in TBLG at angles where the ratio U/t is largest, suggesting a pairing mechanism based on electron-electron interactions.

研究动机与目标

• 推动理解：moiré Superlattice 潜在势在近魔角的扭曲双层石墨烯中如何改变电子谱。
• 在低温下使用 STM/STS 直接绘制 TBLG 的原子尺度结构和局域态密度（LDOS）。
• 识别 van Hove singularities 随扭角和载流子掺杂的演变。
• 评估电子-电子相互作用在塑造低能谱和可能的新兴序中的作用。

提出的方法

• 在绝缘基底上进行 near-magic-angle TBLG 的 tear-and-stack 制备以实现 STM 访问。
• 获取原子分辨率的 STM 拓扑图以识别 AA/AB/SP 区域并提取扭角与应变。
• 采用锁相测量的微分导纳(dI/dV)以获得随能量和位置变化的 LDOS。
• 将实验 LDOS 与经过调整的层内跃迁项以匹配实验费米速度的紧束缚计算进行比较。
• 应用 Hartree-Fock 均场理论以包含 onsite U 和最近邻 V1 相互作用并重现掺杂依赖的 vHs 分裂。

实验结果

研究问题

• RQ1 近魔角 TBLG 中的两个 van Hove singularities 在扭角接近魔角时，其能量间距和宽度如何演化？
• RQ2 电子-电子相互作用（U、V1）在产生相关性诱导的间隙和随掺杂改变 vHs 中的作用为何？
• RQ3 在费米能级附近或与 vHs 对应的能量处，LDOS 中是否存在对称性破缺的证据，如 C3 取向的 nematic 序？
• RQ4 带有现实参数的紧束缚模型在再现观测到的角度与掺杂依赖的 LDOS 特征方面有多好？

主要发现

• LDOS 中观察到两个不同的 van Hove singularities，随着扭角减小而向费米能级移动。
• 1.10° 时 vHs 间距约为 55 meV（实验）和 ~41 meV（理论），且单个 vHs 的宽度在 1.10° 附近达到最小，与超导性相关。
• 在 moderate 掺杂下，当一个 vHs 穿过费米能级时，出现高达 7.5 meV 的相关性诱导间隙。
• 带有 on-site U 和最近邻 V1 的紧束缚模型能够再现观察到的随掺杂变化的 vHs 分裂，得到 U/t ~ 较接近单位量级且 V1 使间隙和分裂与实验匹配。
• STS LDOS 图揭示在费米能级处对称性 C3 的破缺最强，与 nematic 电子相互作用一致。
• 结果表明在 U/t 最大且 vHs 带宽最小的角度，TBLG 可能出现超导性，提示一种电子调控的配对机制。