Abundance of $\mathbb{Z}_2$ topological order in exfoliable two-dimensional insulators

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.