二维可剥离绝缘体中$\mathbb{Z}_2$拓扑序的简化
Abundance of $\mathbb{Z}_2$ topological order in exfoliable two-dimensional insulators
摘要：
量子自旋霍尔绝缘体是一类在体相中具有有限电子带隙和无带隙螺旋边态的二维材料。在时间反演对称性存在的情况下，$\mathbb{Z}_2$拓扑序将拓扑相与普通绝缘相区分开来。从一维低耗散电子输运到自旋过滤，这些材料中可以承载的一些现象可能在电子学、自旋电子学和拓扑量子计算领域的许多技术应用中非常有前途。然而，在室温下可以表现出非平凡的$\mathbb{Z}_2$拓扑顺序的二维材料的稀有性阻碍了发展。在这里，我们筛选了我们最近创建的1825个可以从实验已知化合物剥离的单层的综合数据库，以寻找新的量子自旋霍尔绝缘体。使用密度泛函和多体微扰理论模拟，我们确定了13个单层量子自旋霍尔绝缘体的候选人，包括高性能材料，如AsCuLi $_2$和jacutingaite（Pt $_2$ HgSe $_3$）。我们还确定了单层Pd $_2$ HgSe $_3$作为一种新的Kane-Mele量子自旋霍尔绝缘体，并与jacutingaite比较。这样的少数有前途的材料是机械稳定的，并表现出$\mathbb{Z}_2$拓扑秩序，无论是未扰动或驱动的少量应变。这种筛选突出了约1%的$\mathbb{Z}_2$拓扑顺序的相对丰度，并为实验工作提供了最佳的候选物组。
英文摘要：
Quantum spin Hall insulators are a class of two-dimensional materials with a finite electronic band gap in the bulk and gapless helical edge states. In the presence of time-reversal symmetry, $\mathbb{Z}_2$ topological order distinguishes the topological phase from the ordinary insulating one. Some of the phenomena that can be hosted in these materials, from one-dimensional low-dissipation electronic transport to spin filtering, could be very promising for many technological applications in the fields of electronics, spintronics and topological quantum computing. Nevertheless, the rarity of two-dimensional materials that can exhibit non-trivial $\mathbb{Z}_2$ topological order at room temperature hinders development. Here, we screen a comprehensive database we recently created of 1825 monolayers that can be exfoliated from experimentally known compounds, to search for novel quantum spin Hall insulators. Using density-functional and many-body perturbation theory simulations, we identify 13 monolayers that are candidates for quantum spin Hall insulators, including high-performing materials such as AsCuLi$_2$ and jacutingaite (Pt$_2$HgSe$_3$). We also identify monolayer Pd$_2$HgSe$_3$ as a novel Kane-Mele quantum spin Hall insulator, and compare it with jacutingaite. Such a handful of promising materials are mechanically stable and exhibit $\mathbb{Z}_2$ topological order, either unpertubed or driven by a small amount of strain. Such screening highlights a relative abundance of $\mathbb{Z}_2$ topological order of around 1%, and provides an optimal set of candidates for experimental efforts.
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