Elemental monolayers of group 14 with a buckled honeycomb structure, namely, silicene, germanene, stanene, and plumbene, are known to demonstrate spin splitting as a result of an electric field parallel to their high-symmetry axis, which is capable of tuning their topological phase between a quantum spin Hall insulator and an ordinary band insulator. We perform first-principles calculations based on density functional theory to quantify the spin-dependent band gaps and the spin splitting as a function of the applied electric field and extract the main coefficients of the invariant Hamiltonian. Using linear response theory and the Wannier interpolation method, we calculate the spin Hall conductivity in the monolayers and study its sensitivity to an external electric field. Our results show that the spin Hall conductivity is not quantized and, in the case of silicene, germanene, and stanene, degrades significantly as the electric field inverts the band gap and brings the monolayer into the trivial phase. The electric-field-induced band gap does not close in the case of plumbene with a spin Hall conductivity that is robust to the external electric field.

中文翻译：

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第 14 组屈曲单层中的自旋分裂和自旋霍尔电导率：第一性原理计算

已知具有屈曲蜂窝结构的第 14 族元素单层，即硅烯、锗烯、锡烯和铅烯，由于平行于其高对称轴的电场而表现出自旋分裂，这能够调整其拓扑结构。量子自旋霍尔绝缘体和普通带绝缘体之间的相位。我们执行基于密度泛函理论的第一性原理计算，以量化与自旋相关的带隙和自旋分裂作为外加电场的函数，并提取不变哈密顿量的主要系数。使用线性响应理论和万尼尔插值方法，我们计算了单层中的自旋霍尔电导率并研究了其对外部电场的敏感性。我们的结果表明自旋霍尔电导率没有被量化，并且，在硅烯、锗烯和锡烯的情况下，随着电场反转带隙并使单层进入平凡相，其显着降解。在自旋霍尔电导率对外部电场具有鲁棒性的铅铅的情况下，电场诱导的带隙不会闭合。