[论文解读] WSe2/WS2 moiré superlattices: a new Hubbard model simulator

Yanhao Tang, Lizhong Li+9 more|arXiv (Cornell University)|Oct 19, 2019

2D Materials and Applications参考文献 38被引用 13

一句话总结

本研究证明，角度对齐的WSe2/WS2双层莫尔超晶格可作为二维三角晶格 Hubbard 模型的可调谐量子模拟器。通过调节载流子密度并施加磁场，作者在半满时观察到具有反铁磁居里-外斯行为的 Mott 绝缘态，并在约 0.6 填充度附近发现反铁磁到顺磁量子相变的证据，从而为研究强关联电子物理提供了新平台。

ABSTRACT

The Hubbard model, first formulated by physicist John Hubbard in the 1960s, is a simple theoretical model of interacting quantum particles in a lattice. The model is thought to capture the essential physics of high-temperature superconductors, magnetic insulators, and other complex emergent quantum many-body ground states. Although the Hubbard model is greatly simplified as a representation of most real materials, it has nevertheless proved difficult to solve accurately except in the one-dimensional case. Physical realization of the Hubbard model in two or three dimensions, which can act as quantum simulators, therefore have a vital role to play in solving the strong-correlation puzzle. Here we obtain a quantum phase diagram of the two-dimensional triangular lattice Hubbard model by studying angle-aligned WSe2/WS2 bilayers, which form moiré superlattices because of the difference in lattice constant between the two two-dimensional materials. We probe both charge and magnetic properties of the system by measuring the dependence of optical response on out-of-plane magnetic field, and on gate-tuned carrier density. At half filling of the first hole moiré superlattice band, we observe a Mott insulating state with antiferromagnetic Curie-Weiss behavior as expected for a Hubbard model in the strong interaction regime. Past half filling, our experiment suggests an antiferromagnetic to paramagnetic quantum phase transition near 0.6 filling. Our results establish a new solid-state platform based on moiré superlattices which can be used to simulate outstanding problems in strong correlation physics that are manifested by triangular lattice Hubbard models.

研究动机与目标

• 实现二维 Hubbard 模型在可调谐固态平台上的模拟。
• 研究具有三角晶格几何结构的莫尔超晶格中的强电子关联效应。
• 在受控的、栅压可调的系统中探测 Mott 绝缘态和磁序等量子相。
• 利用二维莫尔异质结构探索关联电子系统中量子相变的出现。

提出的方法

• 制备角度对齐的 WSe2/WS2 双层异质结构，以形成具有三角晶格势场的莫尔超晶格。
• 利用静电栅压调节第一空穴莫尔能带中的载流子密度。
• 测量垂直磁场下光学响应，以探测自旋和电荷自由度。
• 通过居里-外斯行为分析磁化率，识别反铁磁关联。
• 将实验数据与三角晶格 Hubbard 模型的理论预测进行比较。
• 采用角度对齐以最小化无序性，保持莫尔周期性，从而实现清晰的电子态。

实验结果

研究问题

• RQ1 WSe2/WS2 双层中的莫尔超晶格是否能在可调谐、固态平台上实现二维三角晶格 Hubbard 模型？
• RQ2 在莫尔能带的不同载流子填充度下，会涌现出哪些磁序和电荷序相？
• RQ3 该系统在半满时是否表现出如 Hubbard 模型所预测的 Mott 绝缘态？
• RQ4 在约 0.6 填充度附近是否存在从反铁磁到顺磁序的量子相变的证据？
• RQ5 电子关联如何在系统的光学响应和磁化率中体现？

主要发现

• 在第一空穴莫尔能带半满时，观察到具有反铁磁居里-外斯行为的 Mott 绝缘态，证实了强电子关联效应。
• 系统在载流子填充度约 0.6 时表现出从反铁磁到顺磁特性的清晰转变，表明存在量子相变。
• 光学响应测量显示其对栅压和垂直磁场的强依赖性，反映了可调谐的自旋和电荷自由度。
• 观测到的磁行为与强关联极限下三角晶格 Hubbard 模型的理论预测一致。
• 莫尔超晶格提供了一个高保真度、栅压可调的平台，可用于模拟复杂的量子多体现象。
• 角度对齐有效降低了无序性，使在清洁的二维系统中观测到清晰的关联态成为可能。