自发结晶电子态中的子晶格结构与拓扑
Sublattice structure and topology in spontaneously crystallized electronic states
AI总结：
该研究从非平凡量子几何单带模型出发，将自发蜂窝晶格晶体表述为动量空间赝自旋模型，证明额外项可破坏时间反演对称性并稳定量子反常霍尔晶体态。
摘要：
量子反常霍尔效应的预言和实现往往与蜂窝晶格密切相关；在这类晶格中，子晶格自由度在非平凡拓扑中发挥核心作用。另一方面，二维 Wigner 晶体形成没有子晶格自由度的三角晶格，因而产生拓扑平庸态。在这篇 Letter 中，我们讨论了自发形成并表现出量子反常霍尔效应的蜂窝晶格晶体的可能性。从一个具有非平凡量子几何的单带系统出发，我们推导了一类晶体态的平均场能量泛函，并将其表示为动量空间中的子晶格赝自旋模型。我们发现，非平凡量子几何会在赝自旋模型中产生额外项，这些项打破有效的“时间反演对称性”，并有利于形成拓扑非平凡的赝自旋织构。当这些额外项的影响压倒赝自旋之间的铁磁交换耦合时，反常霍尔晶体态在能量上就比平庸的 Wigner 晶体态更有利。
英文摘要：
The prediction and realization of the quantum anomalous Hall effect are often intimately connected to honeycomb lattices in which the sublattice degree of freedom plays a central role in the nontrivial topology. Two-dimensional Wigner crystals, on the other hand, form triangular lattices without sublattice degrees of freedom, resulting in a topologically trivial state. In this Letter, we discuss the possibility of spontaneously formed honeycomb-lattice crystals that exhibit the quantum anomalous Hall effect. Starting from a single-band system with nontrivial quantum geometry, we derive the mean-field energy functional of a class of crystal states and express it as a model of sublattice pseudospins in momentum space. We find that nontrivial quantum geometry leads to extra terms in the pseudospin model that break an effective `time-reversal symmetry' and favor a topologically nontrivial pseudospin texture. When the effects of these extra terms dominate over the ferromagnetic exchange coupling between pseudospins, the anomalous Hall crystal state becomes energetically favorable over the trivial Wigner crystal state.
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