We study free, capped, and encapsulated bilayer jacutingaite $\left({\mathrm{Pt}}_2{\mathrm{HgSe}}_3\right)$ from first principles. While the freestanding bilayer is a large-gap trivial insulator, we find that the encapsulated structure has a small trivial gap due to the competition between sublattice symmetry breaking and sublattice-dependent next-nearest-neighbor hopping. Upon the application of a small perpendicular electric field, the encapsulated bilayer undergoes a topological transition towards a quantum spin Hall insulator. We find that this topological transition can be qualitatively understood by modeling the two layers as uncoupled and can be described by an imbalanced Kane-Mele model that takes into account the sublattice imbalance and the corresponding inversion-symmetry breaking in each layer. Within this picture, bilayer jacutingaite undergoes a transition from a $0+0$ state, where each layer is trivial, to a $0+1$ state, where an unusual topological state relying on Rashba-like spin orbit coupling emerges in only one of the layers.

中文翻译：

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双层jacutingaite封装中的门可调不平衡Kane-Mele模型

我们研究自由的，封端的和封装的双层jacutingaite $（{铂}_{\mathrm{2个}}{\mathrm{汞硒}}_3）$从第一原则。尽管独立双层是一个大间隙的琐碎绝缘子，但我们发现，由于亚格对称性破坏和依赖于子格的下一个最近邻居跳跃之间的竞争，所以封装的结构具有很小的琐细间隙。在施加小的垂直电场时，封装的双层经历了向量子自旋霍尔绝缘体的拓扑转变。我们发现，可以通过将两层建模为未耦合来定性地理解这种拓扑转变，并且可以通过考虑亚晶格不平衡和每一层中相应的反对称性破坏的不平衡Kane-Mele模型来描述。在这张照片中，双层jacutingaite经历了从$0+0$ 状态，其中每一层都是微不足道的 $0+\mathrm{1个}$ 状态，其中依赖于Rashba式自旋轨道耦合的异常拓扑状态仅出现在一层中。